diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results.ipynb
new file mode 100644
index 0000000..c0b1b45
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results.ipynb	
@@ -0,0 +1,271 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Your Turn!\n",
+    "\n",
+    "In the last video, you saw two of the main aspects of principal components:\n",
+    "\n",
+    "1. **The amount of variability captured by the component.**\n",
+    "2. **The components themselves.**\n",
+    "\n",
+    "In this notebook, you will get a chance to explore these a bit more yourself.  First, let's read in the necessary libraries, as well as the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/workspace/helper_functions.py:44: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  mat_data = X.iloc[digit_num].as_matrix().reshape(28,28)  #reshape images\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7acd55ba20>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import show_images, do_pca, scree_plot, plot_component\n",
+    "import test_code as t\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline\n",
+    "\n",
+    "#read in our dataset\n",
+    "train = pd.read_csv('./data/train.csv')\n",
+    "train.fillna(0, inplace=True)\n",
+    "\n",
+    "# save the labels to a Pandas series target\n",
+    "y = train['label']\n",
+    "# Drop the label feature\n",
+    "X = train.drop(\"label\",axis=1)\n",
+    "\n",
+    "show_images(30)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`1.` Perform PCA on the **X** matrix using on your own or using the **do_pca** function from the **helper_functions** module. Reduce the original more than 700 features to only 10 principal components."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Make sure to keep track of the resulting components and the pca object\n",
+    "do_pca?\n",
+    "pca, X_pca = do_pca(10, X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "`2.` Now use the **scree_plot** function from the **helper_functions** module to take a closer look at the results of your analysis."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7a94dc1198>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "scree_plot?\n",
+    "scree_plot(pca)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`3.` Using the results of your scree plot, match each letter as the value to the correct key in the **solution_three** dictionary.  Once you are confident in your solution run the next cell to see if your solution matches ours."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = True\n",
+    "b = False\n",
+    "c = 6.13\n",
+    "d = 'The total amount of variability in the data explained by the first two principal components'\n",
+    "e = None\n",
+    "\n",
+    "solution_three = {\n",
+    "    '10.42' : d,\n",
+    "    'The first component will ALWAYS have the most amount of variability explained.': a,\n",
+    "    'The total amount of variability in the data explained by the first component': c,\n",
+    "    'The sum of the variability explained by all the components can be greater than 100%': b\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Looks good!  The amount of variability explained by each principal component gives us an idea of how much of the original variability in the original data is retained by each component.  Nice job matching these up!\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Run this cell to see if your solution matches ours\n",
+    "t.question_3_check(solution_three)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`4.` Use the **plot_component** function from the **helper_functions** module to look at each of the components (remember they are 0 indexed).  Use the results to assist with question 5."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7a99d90dd8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Use the images of the component weights to answer the next question\n",
+    "plot_component?\n",
+    "plot_component(pca, 3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`5.` Using the results from viewing each of your principal component weights in question 4, change the following values of the **solution_five** dictionary to the **number of the index** for the principal component that best matches the description.  Once you are confident in your solution run the next cell to see if your solution matches ours."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "solution_five = {\n",
+    "    'This component looks like it will assist in identifying zero': 0,\n",
+    "    'This component looks like it will assist in identifying three': 3\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Nice job!  That matches our solution as well!  The index of the first principal component appears to have really high weights where a zero would appear.  Alternatively, the fourth (third indexed component) appears to downweight where a three would appear to make it stand out.\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Run this cell to see if your solution matches ours\n",
+    "t.question_5_check(solution_five)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From this notebook, you have had an opportunity to look at the two major parts of PCA:\n",
+    "\n",
+    "`I.` The amount of **variance explained by each component**.  This is called an **eigenvalue**.\n",
+    "\n",
+    "`II.` The principal components themselves, each component is a vector of weights.  In this case, the principal components help us understand which pixels of the image are most helpful in identifying the difference between between digits. **Principal components** are also known as **eigenvectors**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_SC.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_SC.ipynb
new file mode 100644
index 0000000..5914860
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_SC.ipynb	
@@ -0,0 +1,242 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now that you have seen a bit about how the PCA library works within scikit learn library and fit it to some hand written digits, we should take a closer look at what exactly PCA gives us back to work with and what these different parts mean.  Let's pick up where we left off in the last video.  Below I read in the libraries we used before, split off the image from the label, and I plotted the first 30 images in the dataset."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f0cf357cd68>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import show_images, show_images_by_digit, fit_random_forest_classifier2 \n",
+    "from helper_functions import fit_random_forest_classifier, do_pca, plot_components\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline\n",
+    "\n",
+    "#read in our dataset\n",
+    "train = pd.read_csv('./data/train.csv')\n",
+    "train.fillna(0, inplace=True)\n",
+    "\n",
+    "# save the labels to a Pandas series target\n",
+    "y = train['label']\n",
+    "# Drop the label feature\n",
+    "train.fillna(0, inplace=True)\n",
+    "X = train.drop(\"label\",axis=1)\n",
+    "\n",
+    "show_images(30)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now let's fit PCA with 15 components, and take a look at a few of the main features that live on the pca object we get back."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pca, X_pca = do_pca(15, X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "One of the main features to consider is something called the explained_variance_ratio.  I created what's known as a scree_plot to show the explained_variance_ratio for each of the 15 components."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f0cf4299ba8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def scree_plot(pca):\n",
+    "    '''\n",
+    "    Creates a scree plot associated with the principal components \n",
+    "    \n",
+    "    INPUT: pca - the result of instantian of PCA in scikit learn\n",
+    "            \n",
+    "    OUTPUT:\n",
+    "            None\n",
+    "    '''\n",
+    "    num_components = len(pca.explained_variance_ratio_)\n",
+    "    ind = np.arange(num_components)\n",
+    "    vals = pca.explained_variance_ratio_\n",
+    " \n",
+    "    plt.figure(figsize=(10, 6))\n",
+    "    ax = plt.subplot(111)\n",
+    "    cumvals = np.cumsum(vals)\n",
+    "    ax.bar(ind, vals)\n",
+    "    ax.plot(ind, cumvals)\n",
+    "    for i in range(num_components):\n",
+    "        ax.annotate(r\"%s%%\" % ((str(vals[i]*100)[:4])), (ind[i]+0.2, vals[i]), va=\"bottom\", ha=\"center\", fontsize=12)\n",
+    " \n",
+    "    ax.xaxis.set_tick_params(width=0)\n",
+    "    ax.yaxis.set_tick_params(width=2, length=12)\n",
+    " \n",
+    "    ax.set_xlabel(\"Principal Component\")\n",
+    "    ax.set_ylabel(\"Variance Explained (%)\")\n",
+    "    plt.title('Explained Variance Per Principal Component')\n",
+    "    \n",
+    "\n",
+    "scree_plot(pca)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Each of the bars represents the amount of variability explained by each component.  So you can see the first component explains 5.74% of the variability in the image data.  The second explains 4.11% of the variability and so on.  Often the number of components is chosen based on the total amount of variability explained by the components.  You can see that by using 15 components, we capture almost 35% of the total variability in the images.\n",
+    "\n",
+    "Let's see if we can get a better idea of what aspects of the image the components might be picking up on.  To do this we will work with the components_ attribute of the pca object.  Looking at the shape of components shows us that each component gives the weights for each pixel."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(15, 784)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pca.components_.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "I created a function below to plot the weights of each component in the form of the images.  The darker portions of the image show"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f0d1c7de390>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "def plot_component(pca, comp):\n",
+    "    '''\n",
+    "    Plots an image associated with each component to understand how the weighting \n",
+    "    of the components \n",
+    "    INPUT: \n",
+    "          pca - pca object created from PCA in sklearn\n",
+    "          comp - int - the component you want to see starting at 0\n",
+    "    OUTPUT\n",
+    "          None\n",
+    "    '''\n",
+    "    if comp <= len(pca.components_):\n",
+    "        mat_data = np.asmatrix(pca.components_[comp]).reshape(28,28)  #reshape images\n",
+    "        plt.imshow(mat_data); #plot the data\n",
+    "        plt.xticks([]) #removes numbered labels on x-axis\n",
+    "        plt.yticks([]) #removes numbered labels on y-axis   \n",
+    "    else:\n",
+    "        print('That is not the right input, please read the docstring before continuing.')\n",
+    "        \n",
+    "#Plot the first component\n",
+    "plot_component(pca, 0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Looking at this image, it makes sense that only using two components was able to separate zero better than other digits when looking at this image.  The highest weights are associated with pixels that look a lot like a zero.\n",
+    "\n",
+    "Now, it is your turn!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_Solution.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_Solution.ipynb
new file mode 100644
index 0000000..b61d0ab
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/Interpret_PCA_Results_Solution.ipynb	
@@ -0,0 +1,213 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Your Turn! (Solution)\n",
+    "\n",
+    "In the last video, you saw two of the main aspects of principal components:\n",
+    "\n",
+    "1. **The amount of variability captured by the component.**\n",
+    "2. **The components themselves.**\n",
+    "\n",
+    "In this notebook, you will get a chance to explore these a bit more yourself.  First, let's read in the necessary libraries, as well as the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import show_images, do_pca, scree_plot, plot_component\n",
+    "import test_code as t\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline\n",
+    "\n",
+    "#read in our dataset\n",
+    "train = pd.read_csv('./data/train.csv')\n",
+    "train.fillna(0, inplace=True)\n",
+    "\n",
+    "# save the labels to a Pandas series target\n",
+    "y = train['label']\n",
+    "# Drop the label feature\n",
+    "X = train.drop(\"label\",axis=1)\n",
+    "\n",
+    "show_images(30)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`1.` Perform PCA on the **X** matrix using on your own or using the **do_pca** function from the **helper_functions** module. Reduce the original more than 700 features to only 10 principal components."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pca, X_pca = do_pca(10, X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "`2.` Now use the **scree_plot** function from the **helper_functions** module to take a closer look at the results of your analysis."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "scree_plot(pca)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`3.` Using the results of your scree plot, match each letter as the value to the correct key in the **solution_three** dictionary.  Once you are confident in your solution run the next cell to see if your solution matches ours."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = True\n",
+    "b = False\n",
+    "c = 6.13\n",
+    "d = 'The total amount of variability in the data explained by the first two principal components'\n",
+    "e = None\n",
+    "\n",
+    "solution_three = {\n",
+    "    '10.42' : d, \n",
+    "    'The first component will ALWAYS have the most amount of variability explained.': a,\n",
+    "    'The total amount of variability in the data explained by the first component': c,\n",
+    "    'The sum of the variability explained by all the components can be greater than 100%': b\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Run this cell to see if your solution matches ours\n",
+    "t.question_3_check(solution_three)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`4.` Use the **plot_component** function from the **helper_functions** module to look at each of the components (remember they are 0 indexed).  Use the results to assist with question 5."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot_component(pca, 3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`5.` Using the results from viewing each of your principal component weights in question 4, change the following values of the **solution_five** dictionary to the **number of the index** for the principal component that best matches the description.  Once you are confident in your solution run the next cell to see if your solution matches ours."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "solution_five = {\n",
+    "    'This component looks like it will assist in identifying zero': 0,\n",
+    "    'This component looks like it will assist in identifying three': 3\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Run this cell to see if your solution matches ours\n",
+    "t.question_5_check(solution_five)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From this notebook, you have had an opportunity to look at the two major parts of PCA:\n",
+    "\n",
+    "`I.` The amount of **variance explained by each component**.  This is called an **eigenvalue**.\n",
+    "\n",
+    "`II.` The principal components themselves, each component is a vector of weights.  In this case, the principal components help us understand which pixels of the image are most helpful in identifying the difference between between digits. **Principal components** are also known as **eigenvectors**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1.ipynb
new file mode 100644
index 0000000..9034d2d
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1.ipynb	
@@ -0,0 +1,1176 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Your Turn\n",
+    "\n",
+    "In the previous video, you saw an example of working with some MNIST digits data.  The MNIST dataset can be found here: http://yann.lecun.com/exdb/mnist/.\n",
+    "\n",
+    "First, let's import the necessary libraries.  Notice there are also some imports from a file called `helper_functions`, which contains the functions used in the previous video."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import show_images, show_images_by_digit, fit_random_forest_classifier2 \n",
+    "from helper_functions import fit_random_forest_classifier, do_pca, plot_components\n",
+    "import test_code as t\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`1.` Use pandas to read in the dataset, which can be found in this workspace using the filepath **'./data/train.csv'**.  If you have missing values, fill them with 0.  Take a look at info about the data using `head`, `tail`, `describe`, `info`, etc.  You can learn more about the data values from the article here: https://homepages.inf.ed.ac.uk/rbf/HIPR2/value.htm."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df = pd.read_csv('./data/train.csv')\n",
+    "df.fillna(value=0, inplace=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
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+       "    .dataframe thead th {\n",
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+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>label</th>\n",
+       "      <th>pixel0</th>\n",
+       "      <th>pixel1</th>\n",
+       "      <th>pixel2</th>\n",
+       "      <th>pixel3</th>\n",
+       "      <th>pixel4</th>\n",
+       "      <th>pixel5</th>\n",
+       "      <th>pixel6</th>\n",
+       "      <th>pixel7</th>\n",
+       "      <th>pixel8</th>\n",
+       "      <th>...</th>\n",
+       "      <th>pixel774</th>\n",
+       "      <th>pixel775</th>\n",
+       "      <th>pixel776</th>\n",
+       "      <th>pixel777</th>\n",
+       "      <th>pixel778</th>\n",
+       "      <th>pixel779</th>\n",
+       "      <th>pixel780</th>\n",
+       "      <th>pixel781</th>\n",
+       "      <th>pixel782</th>\n",
+       "      <th>pixel783</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
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+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 785 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  \\\n",
+       "0      1       0       0       0       0       0       0       0       0   \n",
+       "1      0       0       0       0       0       0       0       0       0   \n",
+       "2      1       0       0       0       0       0       0       0       0   \n",
+       "3      4       0       0       0       0       0       0       0       0   \n",
+       "4      0       0       0       0       0       0       0       0       0   \n",
+       "\n",
+       "   pixel8    ...     pixel774  pixel775  pixel776  pixel777  pixel778  \\\n",
+       "0       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "1       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "2       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "3       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "4       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "\n",
+       "   pixel779  pixel780  pixel781  pixel782  pixel783  \n",
+       "0       0.0       0.0       0.0       0.0       0.0  \n",
+       "1       0.0       0.0       0.0       0.0       0.0  \n",
+       "2       0.0       0.0       0.0       0.0       0.0  \n",
+       "3       0.0       0.0       0.0       0.0       0.0  \n",
+       "4       0.0       0.0       0.0       0.0       0.0  \n",
+       "\n",
+       "[5 rows x 785 columns]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.head(5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
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+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>label</th>\n",
+       "      <th>pixel0</th>\n",
+       "      <th>pixel1</th>\n",
+       "      <th>pixel2</th>\n",
+       "      <th>pixel3</th>\n",
+       "      <th>pixel4</th>\n",
+       "      <th>pixel5</th>\n",
+       "      <th>pixel6</th>\n",
+       "      <th>pixel7</th>\n",
+       "      <th>pixel8</th>\n",
+       "      <th>...</th>\n",
+       "      <th>pixel774</th>\n",
+       "      <th>pixel775</th>\n",
+       "      <th>pixel776</th>\n",
+       "      <th>pixel777</th>\n",
+       "      <th>pixel778</th>\n",
+       "      <th>pixel779</th>\n",
+       "      <th>pixel780</th>\n",
+       "      <th>pixel781</th>\n",
+       "      <th>pixel782</th>\n",
+       "      <th>pixel783</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>6304.000000</td>\n",
+       "      <td>6304.0</td>\n",
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+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>4.440355</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.139594</td>\n",
+       "      <td>0.142291</td>\n",
+       "      <td>0.026967</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>2.885613</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>5.099940</td>\n",
+       "      <td>5.531089</td>\n",
+       "      <td>1.675547</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>2.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
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+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>4.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>7.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>9.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>253.000000</td>\n",
+       "      <td>253.000000</td>\n",
+       "      <td>130.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>8 rows × 785 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  \\\n",
+       "count  6304.000000  6304.0  6304.0  6304.0  6304.0  6304.0  6304.0  6304.0   \n",
+       "mean      4.440355     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "std       2.885613     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "min       0.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "25%       2.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "50%       4.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "75%       7.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "max       9.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "\n",
+       "       pixel7  pixel8    ...        pixel774     pixel775     pixel776  \\\n",
+       "count  6304.0  6304.0    ...     6304.000000  6304.000000  6304.000000   \n",
+       "mean      0.0     0.0    ...        0.139594     0.142291     0.026967   \n",
+       "std       0.0     0.0    ...        5.099940     5.531089     1.675547   \n",
+       "min       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "25%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "50%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "75%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "max       0.0     0.0    ...      253.000000   253.000000   130.000000   \n",
+       "\n",
+       "       pixel777  pixel778  pixel779  pixel780  pixel781  pixel782  pixel783  \n",
+       "count    6304.0    6304.0    6304.0    6304.0    6304.0    6304.0    6304.0  \n",
+       "mean        0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "std         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "min         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "25%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "50%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "75%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "max         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "\n",
+       "[8 rows x 785 columns]"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.describe()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`2.` Create a vector called y that holds the **label** column of the dataset.  Store all other columns holding the pixel data of your images in X."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "y = df['label']\n",
+    "X = df.drop('label', axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "That looks right!\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Check Your Solution \n",
+    "t.question_two_check(y, X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`3.` Now use the `show_images_by_digit` function from the `helper_functions` module to take a look some of the `1`'s, `2`'s, `3`'s, or any other value you are interested in looking at.  Do they all look like what you would expect?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/workspace/helper_functions.py:63: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  mat_data = X.iloc[indices[0][digit_num]].as_matrix().reshape(28,28)  #reshape images\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f6be2e500f0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "show_images_by_digit(7) # Try looking at a few other digits"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`4.` Now that you have had a chance to look through some of the data, you can try some different algorithms to see what works well to use the X matrix to predict the response well.  If you would like to use the function I used in the video regarding random forests, you can run the code below, but you might also try any of the supervised techniques you learned in the previous course to see what works best.\n",
+    "\n",
+    "If you decide to put together your own classifier, remember the 4 steps to this process:\n",
+    "\n",
+    "**I.** Instantiate your model. (with all the hyperparameter values you care about)\n",
+    "\n",
+    "**II.** Fit your model. (to the training data)\n",
+    "\n",
+    "**III.** Predict using your fitted model.  (on the test data)\n",
+    "\n",
+    "**IV.** Score your model. (comparing the predictions to the actual values on the test data)\n",
+    "\n",
+    "You can also try a grid search to see if you can improve on your initial predictions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[202   0   0   0   0   0   5   0   2   0]\n",
+      " [  0 234   3   0   0   1   1   2   2   0]\n",
+      " [  1   6 212   1   2   0   0   5   1   0]\n",
+      " [  2   0   6 169   0  10   0   1   2   1]\n",
+      " [  0   0   0   0 171   0   2   1   0   4]\n",
+      " [  2   1   0   5   0 174   3   0   1   0]\n",
+      " [  1   0   0   0   1   2 206   1   0   0]\n",
+      " [  0   0   6   1   7   0   0 204   1   6]\n",
+      " [  0   1   4   7   0   4   1   0 183   2]\n",
+      " [  2   1   0   2   8   1   0   5   6 183]]\n",
+      "0.931283037001\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0.93128303700144166"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Remove the tag to fit the RF model from the video, you can also try fitting your own!\n",
+    "fit_random_forest_classifier(X, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`5.` Now for the purpose of this lesson, to look at PCA.  In the video, I created a model just using two features.  Replicate the process below. You can use the same `do_pca` function that was created in the previous video.  Store your variables in **pca** and **X_pca**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(6304, 11)"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "do_pca?\n",
+    "pca, X_pca = do_pca(11, X)\n",
+    "X_pca.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`6.` The **X_pca** has reduced the original number of more than 700 features down to only 2 features that capture the majority of the variability in the pixel values.  Use the space below to fit a model using these two features to predict the written value.  You can use the random forest model by running `fit_random_forest_classifier` the same way as in the video. How well does it perform?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[189   0   2   0   1   7   7   0   1   2]\n",
+      " [  0 231   2   0   0   0   3   0   7   0]\n",
+      " [  2   2 207   3   3   1   4   3   3   0]\n",
+      " [  1   0  12 157   0   6   1   2  11   1]\n",
+      " [  0   0   2   0 147   1   4   3   1  20]\n",
+      " [  7   0   4   7   3 150   1   0   8   6]\n",
+      " [  6   0   1   0   2   1 200   0   1   0]\n",
+      " [  1   2   4   1   3   1   1 195   5  12]\n",
+      " [  2   2   3   7   3  10   0   1 173   1]\n",
+      " [  3   0   1   2  31   0   0  18   6 147]]\n",
+      "0.863046612206\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0.86304661220567036"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fit_random_forest_classifier?\n",
+    "fit_random_forest_classifier(X_pca, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`7.` Now you can look at the separation of the values using the `plot_components` function.  If you plot all of the points (more than 40,000), you will likely not be able to see much of what is happening.  I recommend plotting just a subset of the data.  Which value(s) have some separation that are being predicted better than others based on these two components?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f6be270c278>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Try plotting some of the numbers below - you can change the number\n",
+    "# of digits that are plotted, but it is probably best not to plot the \n",
+    "# entire dataset.  Your visual will not be readable.\n",
+    "\n",
+    "plot_components(X_pca[:200], y[:200])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`8.` See if you can find a reduced number of features that provides better separation to make predictions.  Say you want to get separation that allows for accuracy of more than 90%, how many principal components are needed to obtain this level of accuracy?  Were you able to substantially reduce the number of features needed in your final model?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[111   0  38  13   7   7  26   0   7   0]\n",
+      " [  0 208   0   4   1   8   4   7   7   4]\n",
+      " [ 38   2  72  25  16  23  35   1  13   3]\n",
+      " [ 13   2  31  18  22  27  25  15  25  13]\n",
+      " [  5   4  18  19  47  17  16  11  10  31]\n",
+      " [  8   8  31  24  14  23  30   3  34  11]\n",
+      " [ 30   4  54  17  13  28  38   2  23   2]\n",
+      " [  3   6   3  10  33   9   3  90   8  60]\n",
+      " [  7   6  23  29  24  32  28   7  36  10]\n",
+      " [  2  12   2  17  29   9   4  54   8  71]]\n",
+      "0.34310427679\n",
+      "[[157   0   6   2   1  11  18   1  13   0]\n",
+      " [  0 224   1   4   2   5   5   0   2   0]\n",
+      " [ 18   3 122  30   5   3  38   0   8   1]\n",
+      " [  3   3  59  54   6  15  27   4  17   3]\n",
+      " [  6   0   2   4  95  15   1  13  16  26]\n",
+      " [  7   0   8  17  22  63  27   7  29   6]\n",
+      " [ 17   8  18  15   2  10 128   0  13   0]\n",
+      " [  0   2   0   4  24   9   1 120   8  57]\n",
+      " [ 15   2   6  29  27  40  36   2  44   1]\n",
+      " [  2   2   1   2  45   4   1  55   8  88]]\n",
+      "0.526189332052\n",
+      "[[175   0   8   0   4  11   4   0   7   0]\n",
+      " [  0 225   1   1   0   2   3   2   9   0]\n",
+      " [ 13   2 167  10   4   8  20   0   3   1]\n",
+      " [  2   0  22 122   0  11   3   1  28   2]\n",
+      " [  5   0   4   1 124   1   7  15   0  21]\n",
+      " [  5   0   5  28  16  81   3   5  34   9]\n",
+      " [  4   0  28   0   2   3 173   0   1   0]\n",
+      " [  3   3   3   1  20   4   0 133   9  49]\n",
+      " [ 14   6   6  29   4  42   1   3  97   0]\n",
+      " [  2   1   2   2  47   6   1  45   7  95]]\n",
+      "0.66890917828\n",
+      "[[176   0   9   0   4   6   5   1   7   1]\n",
+      " [  0 229   2   1   0   2   2   2   4   1]\n",
+      " [ 14   2 176  10   5   8  11   1   1   0]\n",
+      " [  1   0  24 119   0  13   1   2  29   2]\n",
+      " [  3   0   1   0 120   1  10   6   1  36]\n",
+      " [  9   1  10  23   3  93   2   9  31   5]\n",
+      " [  3   0  17   0   3   0 187   0   1   0]\n",
+      " [  2   2   5   3   9   6   0 172   4  22]\n",
+      " [ 14   2   3  19   4  49   2   3 105   1]\n",
+      " [  2   1   2   1  50   8   1  24   4 115]]\n",
+      "0.716962998558\n",
+      "[[177   0   5   0   4  11   8   0   4   0]\n",
+      " [  0 231   2   1   0   1   2   0   6   0]\n",
+      " [  2   2 204   6   5   1   1   2   5   0]\n",
+      " [  0   0  18 134   0  10   2   3  23   1]\n",
+      " [  1   0   3   0 125   1   8   7   1  32]\n",
+      " [  7   0   1  10   2 146   2   4   9   5]\n",
+      " [  4   0   6   1   4   0 195   0   1   0]\n",
+      " [  1   3   7   0  10   1   0 182   4  17]\n",
+      " [  4   3   5  22   6  13   1   2 145   1]\n",
+      " [  0   1   0   0  56   2   1  24  11 113]]\n",
+      "0.793849111004\n",
+      "[[178   0   4   0   4  10   8   0   5   0]\n",
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+      "0.892359442576\n",
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+      " [  4   0   1   0   2   2 201   0   1   0]\n",
+      " [  1   2   6   1   5   0   0 196   2  12]\n",
+      " [  3   1   1  12   2   6   1   0 174   2]\n",
+      " [  2   0   2   3  15   0   0  12   2 172]]\n",
+      "0.894281595387\n",
+      "[[193   0   2   1   1   1   6   3   1   1]\n",
+      " [  0 234   2   1   0   0   2   0   3   1]\n",
+      " [  3   2 207   4   1   0   3   3   4   1]\n",
+      " [  0   0   9 168   0   6   0   2   5   1]\n",
+      " [  0   0   4   0 154   1   4   1   0  14]\n",
+      " [  2   0   3   7   1 165   2   0   3   3]\n",
+      " [  6   0   1   0   1   1 201   0   1   0]\n",
+      " [  0   0   7   1   6   0   0 196   3  12]\n",
+      " [  0   1   1  12   0   6   1   0 178   3]\n",
+      " [  2   0   2   3  18   0   0  16   1 166]]\n",
+      "0.89476213359\n",
+      "[[191   0   4   1   1   1   7   1   1   2]\n",
+      " [  0 234   2   0   0   1   2   0   3   1]\n",
+      " [  2   2 208   3   2   0   4   3   4   0]\n",
+      " [  0   0   8 169   0   5   0   2   7   0]\n",
+      " [  0   0   3   0 157   1   3   1   0  13]\n",
+      " [  1   0   3   7   2 166   1   0   2   4]\n",
+      " [  2   0   2   0   3   2 202   0   0   0]\n",
+      " [  0   1   7   1   4   0   0 194   2  16]\n",
+      " [  0   1   1  12   1   5   0   1 181   0]\n",
+      " [  1   0   1   2  14   1   0  14   2 173]]\n",
+      "0.901009130226\n",
+      "With only 25 components, a random forest acheived an accuracy of 0.9010091302258529.\n"
+     ]
+    }
+   ],
+   "source": [
+    "for comp in range(2, 100):\n",
+    "    pca, X_pca = do_pca(comp, X)\n",
+    "    acc = fit_random_forest_classifier(X_pca, y)\n",
+    "    if acc > .90:\n",
+    "        print(\"With only {} components, a random forest acheived an accuracy of {}.\".format(comp, acc))\n",
+    "        break"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`9.` It is possible that extra features in the dataset even lead to overfitting or the [curse of dimensionality](https://stats.stackexchange.com/questions/65379/machine-learning-curse-of-dimensionality-explained).  Do you have evidence of this happening for this dataset?  Can you support your evidence with a visual or table?  To avoid printing out all of the metric results, I created another function called `fit_random_forest_classifier2`.  I ran through a significant number of components to create the visual for the solution, but I strongly recommend you look in the range below 100 principal components!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# I would highly recommend not running the below code, as it had to run overnight to complete.\n",
+    "# Instead, you can run a smaller number of components that still allows you to see enough.\n",
+    "\n",
+    "\n",
+    "#accs = []\n",
+    "#comps = []\n",
+    "#for comp in range(2, 700):\n",
+    "#    comps.append(comp)\n",
+    "#    pca, X_pca = do_pca(comp, X)\n",
+    "#    acc = fit_random_forest_classifier2(X_pca, y)\n",
+    "#    accs.append(acc)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'comps' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-45-d11575a86762>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcomps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'bo'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Number of Components'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Accuracy'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Number of Components by Accuracy'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'comps' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "plt.plot(comps, accs, 'bo');\n",
+    "plt.xlabel('Number of Components');\n",
+    "plt.ylabel('Accuracy');\n",
+    "plt.title('Number of Components by Accuracy');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1_Solution.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1_Solution.ipynb
new file mode 100644
index 0000000..1787fa6
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_1_Solution.ipynb	
@@ -0,0 +1,500 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Your Turn\n",
+    "\n",
+    "In the previous video, you saw an example of working with some MNIST digits data.  A link to the dataset can be found here: http://yann.lecun.com/exdb/mnist/.\n",
+    "\n",
+    "First, let's import the necessary libraries.  Notice, there are also some imports from a file called `helper_functions`, which contains the functions used in the previous video."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import show_images, show_images_by_digit, fit_random_forest_classifier2 \n",
+    "from helper_functions import fit_random_forest_classifier, do_pca, plot_components\n",
+    "import test_code as t\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`1.` Use pandas to read in the dataset, which can be found at the following address **'./data/train.csv'**.  Take a look at info about the data using `head`, `tail`, `describe`, `info`, etc.  You can learn more about the data values from the article here: https://homepages.inf.ed.ac.uk/rbf/HIPR2/value.htm."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "train = pd.read_csv('./data/train.csv')\n",
+    "train.fillna(0, inplace=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`2.` Create a vector called **y** that holds the **label** column of the dataset.  Store all other columns holding the pixel data of your images in **X**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# save the labels to a Pandas series target\n",
+    "y = train['label']\n",
+    "\n",
+    "# Drop the label feature\n",
+    "X = train.drop(\"label\",axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "That looks right!\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Check Your Solution \n",
+    "t.question_two_check(y, X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`3.` Now use the `show_images_by_digit` function from the `helper_functions` module to take a look some of the `1`'s, `2`'s, `3`'s, or any other value you are interested in looking at.  Do they all look like what you would expect?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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cEZLGy8XFBadOnbKahzmcOXNGOJFehkdpaSlCQkKEvCMiHDlyxO4ewItHe09P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\noVAoHoQGXQqFQvEgNOhSKBSKB/k/lV7irwKNfjIAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x115a3da20>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "show_images_by_digit(2) # Try looking at a few other digits"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`4.` Now that you have had a chance to look through some of the data, you can try some different algorithms to see what works well to use the X matrix to predict the response well.  If you would like to use the function I used in the video regarding random forests, you can run the code below, but you might also try any of the supervised techniques you learned in the previous course to see what works best.\n",
+    "\n",
+    "If you decide to put together your own classifier, remember the 4 steps to this process:\n",
+    "\n",
+    "**I.** Instantiate your model. (with all the hyperparameter values you care about)\n",
+    "\n",
+    "**II.** Fit your model. (to the training data)\n",
+    "\n",
+    "**III.** Predict using your fitted model.  (on the test data)\n",
+    "\n",
+    "**IV.** Score your model. (comparing the predictions to the actual values on the test data)\n",
+    "\n",
+    "You can also try a grid search to see if you can improve on your initial predictions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1317    0    2    0    2    1    5    0    6    0]\n",
+      " [   1 1501    5    3    2    2    3    1    1    1]\n",
+      " [   6    4 1354    8   13    1    7   10   10    1]\n",
+      " [   6    3   13 1378    3   22    2   16   18   10]\n",
+      " [   4    0    1    0 1311    0    7    3    3   29]\n",
+      " [   6    2    2   18    2 1149   10    1    8    7]\n",
+      " [   9    3    1    0    4    8 1366    0    6    0]\n",
+      " [   1    8   23    2   10    1    0 1405    4   26]\n",
+      " [   3    5    6   11    7    6    5    3 1273   15]\n",
+      " [   6    4    4   20   11    4    2    9   13 1275]]\n",
+      "0.961688311688\n"
+     ]
+    }
+   ],
+   "source": [
+    "fit_random_forest_classifier(X, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`5.` Now the purpose of this lesson, to look at PCA.  In the video, I created a model just using two features.  Replicate the process below. You can use the same `do_pca` function that was created in the previous video.  Store your variables in **pca** and **X_pca**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pca, X_pca = do_pca(2, X) #performs PCA to create two components"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`6.` The **X_pca** has moved the original more than 700 features down to only 2 features that capture the majority of the variability in the pixel values.  Use the space below to fit a model using these two features to predict the written value.  You can use the random forest model by running `fit_random_forest_classifier` the same way as in the video. How well does it perform?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 828    0  181   49   32   44  139    8   40   12]\n",
+      " [   1 1291    2   16   28   34   19   44   38   47]\n",
+      " [ 228    5  305  194  130  119  204   52  121   56]\n",
+      " [  79   26  207  222  149  178  172  143  174  121]\n",
+      " [  51   60  120  163  226  111  123  171  129  204]\n",
+      " [  64   22  133  131  135  228  191   48  194   59]\n",
+      " [ 203   28  218  159  112  203  279   33  129   33]\n",
+      " [   9   81   60  112  177   74   30  527   78  332]\n",
+      " [  57   51  119  158  138  224  154   86  230  117]\n",
+      " [  15  110   61   96  206   62   50  312   71  365]]\n",
+      "0.324747474747\n"
+     ]
+    }
+   ],
+   "source": [
+    "fit_random_forest_classifier(X_pca, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`7.` Now you can look at the separation of the values using the `plot_components` function.  If you plot all of the points (more than 40,000), you will likely not be able to see much of what is happening.  I recommend plotting just a subset of the data.  Which value(s) have some separation that are being predicted better than others based on these two components?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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H/zopQRIhx2kv/5BE6PdVwT8rjclOP2hqS5D8exu01bu7vd5e3fmu3HswwZKLzLgsrJ+0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\ngPMIHgAA4Lx/AElaJdJUU9vGAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x116fdf208>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_components(X_pca[:100], y[:100])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`8.` See if you can find a reduced number of features that provides better separation to make predictions.  Say you want to get separation that allows for accuracy of more than 90%, how many principal components are needed to obtain this level of accuracy?  Were you able to substantially reduce the number of features needed in your final model?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 820    0  179   51   33   50  140    5   47    8]\n",
+      " [   1 1294    3   14   30   33   20   50   35   40]\n",
+      " [ 224    5  316  205  129  111  200   54  116   54]\n",
+      " [  79   22  199  223  146  189  172  146  169  126]\n",
+      " [  52   58  128  164  223  113  120  163  131  206]\n",
+      " [  63   24  133  127  139  227  192   43  201   56]\n",
+      " [ 190   28  228  157  104  196  284   32  145   33]\n",
+      " [   9   79   66  113  175   67   35  522   81  333]\n",
+      " [  51   54  129  159  138  210  155   84  232  122]\n",
+      " [  16  113   62  103  192   59   55  310   74  364]]\n",
+      "0.325036075036\n",
+      "[[1002    0   37   12   22   51  151    0   57    1]\n",
+      " [   0 1420    6   14    5    5   25    2   40    3]\n",
+      " [  93    4  671  307   29   65  184    0   58    3]\n",
+      " [  22   24  333  573   50   85  179   33  155   17]\n",
+      " [  44   12    8   22  752   79   12   97   53  279]\n",
+      " [  58    4   88  104  174  384  151   21  178   43]\n",
+      " [ 210   34  121   94   17   76  739    2  104    0]\n",
+      " [   4   23    0   27  194   30    7  813   20  362]\n",
+      " [  58   39   61  192  141  266  215   18  320   24]\n",
+      " [  12    3    1   19  321   31    6  293   17  645]]\n",
+      "0.528066378066\n",
+      "[[1157    0   48    3   25   31   17    2   49    1]\n",
+      " [   1 1444    9    3    2    2   12    6   37    4]\n",
+      " [  92    7  945   87   34   30  171    4   42    2]\n",
+      " [  18   11   95  986    9  123   11   20  185   13]\n",
+      " [  22   10   17    1  894   38   21   81    9  265]\n",
+      " [  39    3   59  142   68  540   15   35  266   38]\n",
+      " [  33    8  121    3   19   11 1183    0   19    0]\n",
+      " [   4   26    6   12  120   32    2  891   51  336]\n",
+      " [  81   42   31  176   32  272   12   29  632   27]\n",
+      " [  14    3    3   13  282   30    2  257   32  712]]\n",
+      "0.677056277056\n",
+      "[[1182    0   38    2   11   20   21    3   56    0]\n",
+      " [   1 1463   14    7    0    5    4    6   17    3]\n",
+      " [  60    3 1093   87   22   22   84    7   34    2]\n",
+      " [  17   10   96 1040   11  124    6   26  135    6]\n",
+      " [  13    9   15    3  951    7   17   50   10  283]\n",
+      " [  41    4   51  150   25  590   10   63  254   17]\n",
+      " [  37    4   83    1   17    8 1224    0   23    0]\n",
+      " [   4   26    9   19   58   24    3 1193   23  121]\n",
+      " [  70   22   22  116   27  228   13   18  788   30]\n",
+      " [  11    3    1   10  276   28    4  121   25  869]]\n",
+      "0.749855699856\n",
+      "[[1218    0    5    4   10   38   25    0   32    1]\n",
+      " [   1 1483    9    8    0    2    5    2    6    4]\n",
+      " [  14    1 1247   43   24    3   21    9   52    0]\n",
+      " [   7   12   51 1101   10   89    9   32  153    7]\n",
+      " [   7   11   20    0 1001    5   16   32   14  252]\n",
+      " [  43    1    5  110   23  907   25   16   66    9]\n",
+      " [  37    4   23    2   16   10 1292    0   13    0]\n",
+      " [   2   13   20    6   50    3    0 1265   21  100]\n",
+      " [  20   12   28  111   36   61   14   17 1014   21]\n",
+      " [   9    5    2   15  257   15    2   96   31  916]]\n",
+      "0.825685425685\n",
+      "[[1220    0    5    4   12   35   24    0   33    0]\n",
+      " [   0 1489    8    6    0    1    5    2    5    4]\n",
+      " [  16    4 1253   38   22    3   24   10   44    0]\n",
+      " [  12   14   51 1164   14   66    6   25  112    7]\n",
+      " [   2   10   18    3 1024    7   16   29   12  237]\n",
+      " [  39    2    6  113   26  917   26   17   49   10]\n",
+      " [  44    4   23    2   14   14 1288    0    8    0]\n",
+      " [   1   11   15    6   41    4    0 1284   24   94]\n",
+      " [  19   15   26  101   29   51   15   14 1043   21]\n",
+      " [   9    4    3   14  245   15    2   89   35  932]]\n",
+      "0.837950937951\n",
+      "[[1268    0    5    5    2   23   20    2    8    0]\n",
+      " [   1 1493    8    7    0    2    5    2    0    2]\n",
+      " [  17    2 1271   35   18    7   20    9   34    1]\n",
+      " [  10   11   38 1221    8   51    4   21   95   12]\n",
+      " [   3    7   18    6 1064    8   15   17    9  211]\n",
+      " [  36    2   10   76   22  966   22    3   54   14]\n",
+      " [  38    3   16    2   12   16 1303    0    7    0]\n",
+      " [   1   13   15    6   31    2    0 1321   11   80]\n",
+      " [  12   14   19   65   30   57    9    4 1102   22]\n",
+      " [   8    4    5   18  238   10    2   87   33  943]]\n",
+      "0.862337662338\n",
+      "[[1265    0    6    1    1   21   25    2   12    0]\n",
+      " [   1 1487    8    6    1    3    5    1    1    7]\n",
+      " [  14    3 1282   37   20    2   11   13   32    0]\n",
+      " [   9   10   39 1239    7   44    5   23   83   12]\n",
+      " [   4    9   14    5 1078    7   14   13   13  201]\n",
+      " [  25    2    7   62   18 1016   20    2   40   13]\n",
+      " [  41    4    8    0    7    9 1320    0    8    0]\n",
+      " [   0   13   19   10   25    1    0 1325   10   77]\n",
+      " [  10   10   15   42   34   50   10    7 1139   17]\n",
+      " [  10    4    3   21  212    7    2   75   27  987]]\n",
+      "0.875757575758\n",
+      "[[1267    1    5    2    2   25   20    1    9    1]\n",
+      " [   0 1490    8    3    1    3    6    2    2    5]\n",
+      " [  16    2 1296   29   12    2   11   14   31    1]\n",
+      " [   8    9   36 1265    2   43    3   22   69   14]\n",
+      " [   4    7   11    2 1161    4   12   10    8  139]\n",
+      " [  25    1    4   58   16 1019   25    3   38   16]\n",
+      " [  31    4    8    0    9   12 1325    0    8    0]\n",
+      " [   1   12   17   10   11    2    0 1338   13   76]\n",
+      " [  11   13   17   31   19   42    9    6 1169   17]\n",
+      " [  11    4    4   21  106   11    2   62   24 1103]]\n",
+      "0.897041847042\n",
+      "[[1282    0    5    0    2   17   18    0    7    2]\n",
+      " [   0 1491    7    4    1    2    6    1    2    6]\n",
+      " [  16    1 1299   29   12    3    8   12   33    1]\n",
+      " [   6    8   31 1282    2   39    4   23   63   13]\n",
+      " [   2    7   13    2 1177    2   12   12    8  123]\n",
+      " [  18    1    6   62   12 1024   19    3   42   18]\n",
+      " [  22    4    6    1    9   14 1334    0    7    0]\n",
+      " [   0   13   19    9   13    2    0 1336   15   73]\n",
+      " [   6   11   11   32   20   46    8    5 1179   16]\n",
+      " [  12    2    3   23   92    5    2   66   25 1118]]\n",
+      "0.903463203463\n",
+      "With only 11 components, a random forest acheived an accuracy of 0.9034632034632034.\n"
+     ]
+    }
+   ],
+   "source": [
+    "for comp in range(2, 100):\n",
+    "    pca, X_pca = do_pca(comp, X)\n",
+    "    acc = fit_random_forest_classifier(X_pca, y)\n",
+    "    if acc > .90:\n",
+    "        print(\"With only {} components, a random forest acheived an accuracy of {}.\".format(comp, acc))\n",
+    "        break"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`9.` It is possible that extra features in the dataset even lead to overfitting or the [curse of dimensionality](https://stats.stackexchange.com/questions/65379/machine-learning-curse-of-dimensionality-explained).  Do you have evidence of this happening for this dataset?  Can you support your evidence with a visual or table?  To avoid printing out all of the metric results, I created another function called `fit_random_forest_classifier2`.  I ran through a significant number of components to create the visual for the solution, but I strongly recommend you look in the range below 100 principal components!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# I would highly recommend not running the below code, as it had to run overnight to complete.\n",
+    "# Instead, you can run a smaller number of components that still allows you to see enough.\n",
+    "\n",
+    "\n",
+    "#accs = []\n",
+    "#comps = []\n",
+    "#for comp in range(2, 700):\n",
+    "#    comps.append(comp)\n",
+    "#    pca, X_pca = do_pca(comp, X)\n",
+    "#    acc = fit_random_forest_classifier2(X_pca, y)\n",
+    "#    accs.append(acc)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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RzYIFa2hv7yGXg/b2HhYs0ACwiEhRw94FBCEJdHR009Y2nq6uV0c6HBGRmtKw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\nYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1394e07f0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(comps, accs, 'bo');\n",
+    "plt.xlabel('Number of Components');\n",
+    "plt.ylabel('Accuracy');\n",
+    "plt.title('Number of Components by Accuracy');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.94126984126984126, 61)"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# The max accuracy and corresponding number of components\n",
+    "np.max(accs), comps[np.where(accs == np.max(accs))[0][0]]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Here you can see that the accuracy quickly levels off.  The maximum accuracy is actually acheived at 61 principal components.  Given the slight negative trend also indicates that the final components are mostly containing noise.  The 61 components here contain the information needed to be able to determine the images nearly to the same ability as using the entire image.  Next, let's take a closer look at exactly what other information we get from PCA, and how we can interpret it.** "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_Mini_Project.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_Mini_Project.ipynb
new file mode 100644
index 0000000..cb69686
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_Mini_Project.ipynb	
@@ -0,0 +1,1092 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### PCA Mini Project\n",
+    "\n",
+    "In the lesson, you saw how you could use PCA to substantially reduce the dimensionality of the handwritten digits.  In this mini-project, you will be using the **cars.csv** file.  \n",
+    "\n",
+    "To begin, run the cell below to read in the necessary libraries and the dataset.  I also read in the helper functions that you used throughout the lesson in case you might find them helpful in completing this project.  Otherwise, you can always create functions of your own!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "from helper_functions import do_pca, scree_plot, plot_components, pca_results\n",
+    "from IPython import display\n",
+    "import test_code2 as t\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline\n",
+    "\n",
+    "df = pd.read_csv('./data/cars.csv')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`1.` Now your data is stored in **df**.  Use the below cells to take a look your dataset.  At the end of your exploration, use your findings to match the appropriate variable to each key in the dictionary below.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Sports</th>\n",
+       "      <th>SUV</th>\n",
+       "      <th>Wagon</th>\n",
+       "      <th>Minivan</th>\n",
+       "      <th>Pickup</th>\n",
+       "      <th>AWD</th>\n",
+       "      <th>RWD</th>\n",
+       "      <th>Retail</th>\n",
+       "      <th>Dealer</th>\n",
+       "      <th>Engine</th>\n",
+       "      <th>Cylinders</th>\n",
+       "      <th>Horsepower</th>\n",
+       "      <th>CityMPG</th>\n",
+       "      <th>HighwayMPG</th>\n",
+       "      <th>Weight</th>\n",
+       "      <th>Wheelbase</th>\n",
+       "      <th>Length</th>\n",
+       "      <th>Width</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Acura 3.5 RL</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>43755</td>\n",
+       "      <td>39014</td>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>225</td>\n",
+       "      <td>18</td>\n",
+       "      <td>24</td>\n",
+       "      <td>3880</td>\n",
+       "      <td>115</td>\n",
+       "      <td>197</td>\n",
+       "      <td>72</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Acura 3.5 RL Navigation</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>46100</td>\n",
+       "      <td>41100</td>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>225</td>\n",
+       "      <td>18</td>\n",
+       "      <td>24</td>\n",
+       "      <td>3893</td>\n",
+       "      <td>115</td>\n",
+       "      <td>197</td>\n",
+       "      <td>72</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Acura MDX</th>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>36945</td>\n",
+       "      <td>33337</td>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>265</td>\n",
+       "      <td>17</td>\n",
+       "      <td>23</td>\n",
+       "      <td>4451</td>\n",
+       "      <td>106</td>\n",
+       "      <td>189</td>\n",
+       "      <td>77</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Acura NSX S</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>89765</td>\n",
+       "      <td>79978</td>\n",
+       "      <td>3.2</td>\n",
+       "      <td>6</td>\n",
+       "      <td>290</td>\n",
+       "      <td>17</td>\n",
+       "      <td>24</td>\n",
+       "      <td>3153</td>\n",
+       "      <td>100</td>\n",
+       "      <td>174</td>\n",
+       "      <td>71</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Acura RSX</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>23820</td>\n",
+       "      <td>21761</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>200</td>\n",
+       "      <td>24</td>\n",
+       "      <td>31</td>\n",
+       "      <td>2778</td>\n",
+       "      <td>101</td>\n",
+       "      <td>172</td>\n",
+       "      <td>68</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                         Sports  SUV  Wagon  Minivan  Pickup  AWD  RWD  \\\n",
+       "Acura 3.5 RL                  0    0      0        0       0    0    0   \n",
+       "Acura 3.5 RL Navigation       0    0      0        0       0    0    0   \n",
+       "Acura MDX                     0    1      0        0       0    1    0   \n",
+       "Acura NSX S                   1    0      0        0       0    0    1   \n",
+       "Acura RSX                     0    0      0        0       0    0    0   \n",
+       "\n",
+       "                         Retail  Dealer  Engine  Cylinders  Horsepower  \\\n",
+       "Acura 3.5 RL              43755   39014     3.5          6         225   \n",
+       "Acura 3.5 RL Navigation   46100   41100     3.5          6         225   \n",
+       "Acura MDX                 36945   33337     3.5          6         265   \n",
+       "Acura NSX S               89765   79978     3.2          6         290   \n",
+       "Acura RSX                 23820   21761     2.0          4         200   \n",
+       "\n",
+       "                         CityMPG  HighwayMPG  Weight  Wheelbase  Length  Width  \n",
+       "Acura 3.5 RL                  18          24    3880        115     197     72  \n",
+       "Acura 3.5 RL Navigation       18          24    3893        115     197     72  \n",
+       "Acura MDX                     17          23    4451        106     189     77  \n",
+       "Acura NSX S                   17          24    3153        100     174     71  \n",
+       "Acura RSX                     24          31    2778        101     172     68  "
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Sports</th>\n",
+       "      <th>SUV</th>\n",
+       "      <th>Wagon</th>\n",
+       "      <th>Minivan</th>\n",
+       "      <th>Pickup</th>\n",
+       "      <th>AWD</th>\n",
+       "      <th>RWD</th>\n",
+       "      <th>Retail</th>\n",
+       "      <th>Dealer</th>\n",
+       "      <th>Engine</th>\n",
+       "      <th>Cylinders</th>\n",
+       "      <th>Horsepower</th>\n",
+       "      <th>CityMPG</th>\n",
+       "      <th>HighwayMPG</th>\n",
+       "      <th>Weight</th>\n",
+       "      <th>Wheelbase</th>\n",
+       "      <th>Length</th>\n",
+       "      <th>Width</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.0</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "      <td>387.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>0.116279</td>\n",
+       "      <td>0.152455</td>\n",
+       "      <td>0.072351</td>\n",
+       "      <td>0.054264</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.201550</td>\n",
+       "      <td>0.242894</td>\n",
+       "      <td>33231.180879</td>\n",
+       "      <td>30440.653747</td>\n",
+       "      <td>3.127390</td>\n",
+       "      <td>5.757106</td>\n",
+       "      <td>214.444444</td>\n",
+       "      <td>20.312661</td>\n",
+       "      <td>27.263566</td>\n",
+       "      <td>3532.457364</td>\n",
+       "      <td>107.211886</td>\n",
+       "      <td>184.961240</td>\n",
+       "      <td>71.276486</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.320974</td>\n",
+       "      <td>0.359926</td>\n",
+       "      <td>0.259404</td>\n",
+       "      <td>0.226830</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.401677</td>\n",
+       "      <td>0.429387</td>\n",
+       "      <td>19724.634576</td>\n",
+       "      <td>17901.179282</td>\n",
+       "      <td>1.014314</td>\n",
+       "      <td>1.490182</td>\n",
+       "      <td>70.262822</td>\n",
+       "      <td>5.262333</td>\n",
+       "      <td>5.636005</td>\n",
+       "      <td>706.003622</td>\n",
+       "      <td>7.086553</td>\n",
+       "      <td>13.237999</td>\n",
+       "      <td>3.368329</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>10280.000000</td>\n",
+       "      <td>9875.000000</td>\n",
+       "      <td>1.400000</td>\n",
+       "      <td>3.000000</td>\n",
+       "      <td>73.000000</td>\n",
+       "      <td>10.000000</td>\n",
+       "      <td>12.000000</td>\n",
+       "      <td>1850.000000</td>\n",
+       "      <td>89.000000</td>\n",
+       "      <td>143.000000</td>\n",
+       "      <td>64.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>20997.000000</td>\n",
+       "      <td>19575.000000</td>\n",
+       "      <td>2.300000</td>\n",
+       "      <td>4.000000</td>\n",
+       "      <td>165.000000</td>\n",
+       "      <td>18.000000</td>\n",
+       "      <td>24.000000</td>\n",
+       "      <td>3107.000000</td>\n",
+       "      <td>103.000000</td>\n",
+       "      <td>177.000000</td>\n",
+       "      <td>69.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>28495.000000</td>\n",
+       "      <td>26155.000000</td>\n",
+       "      <td>3.000000</td>\n",
+       "      <td>6.000000</td>\n",
+       "      <td>210.000000</td>\n",
+       "      <td>19.000000</td>\n",
+       "      <td>27.000000</td>\n",
+       "      <td>3469.000000</td>\n",
+       "      <td>107.000000</td>\n",
+       "      <td>186.000000</td>\n",
+       "      <td>71.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>39552.500000</td>\n",
+       "      <td>36124.000000</td>\n",
+       "      <td>3.800000</td>\n",
+       "      <td>6.000000</td>\n",
+       "      <td>250.000000</td>\n",
+       "      <td>21.500000</td>\n",
+       "      <td>30.000000</td>\n",
+       "      <td>3922.000000</td>\n",
+       "      <td>112.000000</td>\n",
+       "      <td>193.000000</td>\n",
+       "      <td>73.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>192465.000000</td>\n",
+       "      <td>173560.000000</td>\n",
+       "      <td>6.000000</td>\n",
+       "      <td>12.000000</td>\n",
+       "      <td>493.000000</td>\n",
+       "      <td>60.000000</td>\n",
+       "      <td>66.000000</td>\n",
+       "      <td>6400.000000</td>\n",
+       "      <td>130.000000</td>\n",
+       "      <td>221.000000</td>\n",
+       "      <td>81.000000</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "           Sports         SUV       Wagon     Minivan  Pickup         AWD  \\\n",
+       "count  387.000000  387.000000  387.000000  387.000000   387.0  387.000000   \n",
+       "mean     0.116279    0.152455    0.072351    0.054264     0.0    0.201550   \n",
+       "std      0.320974    0.359926    0.259404    0.226830     0.0    0.401677   \n",
+       "min      0.000000    0.000000    0.000000    0.000000     0.0    0.000000   \n",
+       "25%      0.000000    0.000000    0.000000    0.000000     0.0    0.000000   \n",
+       "50%      0.000000    0.000000    0.000000    0.000000     0.0    0.000000   \n",
+       "75%      0.000000    0.000000    0.000000    0.000000     0.0    0.000000   \n",
+       "max      1.000000    1.000000    1.000000    1.000000     0.0    1.000000   \n",
+       "\n",
+       "              RWD         Retail         Dealer      Engine   Cylinders  \\\n",
+       "count  387.000000     387.000000     387.000000  387.000000  387.000000   \n",
+       "mean     0.242894   33231.180879   30440.653747    3.127390    5.757106   \n",
+       "std      0.429387   19724.634576   17901.179282    1.014314    1.490182   \n",
+       "min      0.000000   10280.000000    9875.000000    1.400000    3.000000   \n",
+       "25%      0.000000   20997.000000   19575.000000    2.300000    4.000000   \n",
+       "50%      0.000000   28495.000000   26155.000000    3.000000    6.000000   \n",
+       "75%      0.000000   39552.500000   36124.000000    3.800000    6.000000   \n",
+       "max      1.000000  192465.000000  173560.000000    6.000000   12.000000   \n",
+       "\n",
+       "       Horsepower     CityMPG  HighwayMPG       Weight   Wheelbase  \\\n",
+       "count  387.000000  387.000000  387.000000   387.000000  387.000000   \n",
+       "mean   214.444444   20.312661   27.263566  3532.457364  107.211886   \n",
+       "std     70.262822    5.262333    5.636005   706.003622    7.086553   \n",
+       "min     73.000000   10.000000   12.000000  1850.000000   89.000000   \n",
+       "25%    165.000000   18.000000   24.000000  3107.000000  103.000000   \n",
+       "50%    210.000000   19.000000   27.000000  3469.000000  107.000000   \n",
+       "75%    250.000000   21.500000   30.000000  3922.000000  112.000000   \n",
+       "max    493.000000   60.000000   66.000000  6400.000000  130.000000   \n",
+       "\n",
+       "           Length       Width  \n",
+       "count  387.000000  387.000000  \n",
+       "mean   184.961240   71.276486  \n",
+       "std     13.237999    3.368329  \n",
+       "min    143.000000   64.000000  \n",
+       "25%    177.000000   69.000000  \n",
+       "50%    186.000000   71.000000  \n",
+       "75%    193.000000   73.000000  \n",
+       "max    221.000000   81.000000  "
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.describe()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(387, 18)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.054263565891472867"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df['Minivan'].sum()/387"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = 7\n",
+    "b = 66\n",
+    "c = 387\n",
+    "d = 18\n",
+    "e = 0.23\n",
+    "f = 0.05\n",
+    "\n",
+    "solution_1_dict = {\n",
+    "    'The number of cars in the dataset': c,\n",
+    "    'The number of car features in the dataset': d,\n",
+    "    'The number of dummy variables in the dataset': a,\n",
+    "    'The proportion of minivans in the dataset': f,\n",
+    "    'The max highway mpg for any car': b\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Nice job!  Looks like your dataset matches what we found!\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"https://bit.ly/2K9X0gD\">"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Check your solution against ours by running this cell\n",
+    "display.HTML(t.check_question_one(solution_1_dict))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`2.` There are some particularly nice properties about PCA to keep in mind.  Use the dictionary below to match the correct variable as the key to each statement.  When you are ready, check your solution against ours by running the following cell."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = True\n",
+    "b = False\n",
+    "\n",
+    "solution_2_dict = {\n",
+    "    'The components span the directions of maximum variability.': a,\n",
+    "    'The components are always orthogonal to one another.': a,\n",
+    "    'Eigenvalues tell us the amount of information a component holds': a\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "That's right these are all true.  Principal components are orthogonal, span the directions of maximum variability, and the corresponding eigenvalues tell us how much of the original variability is explained by each component.\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Check your solution against ours by running this cell\n",
+    "t.check_question_two(solution_2_dict)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`3.` Fit PCA to reduce the current dimensionality of the datset to 3 dimensions.  You can use the helper functions, or perform the steps on your own.  If you fit on your own, be sure to standardize your data.  At the end of this process, you will want an X matrix with the reduced dimensionality to only 3 features.  Additionally, you will want your **pca** object back that has been used to fit and transform your dataset. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Scale your data, fit, and transform using pca\n",
+    "pca, X_pca = do_pca(3, df)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`4.` Once you have your pca object, you can take a closer look at what comprises each of the principal components.  Use the **pca_results** function from the **helper_functions** module assist with taking a closer look at the results of your analysis.  The function takes two arguments: the full dataset and the pca object you created."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Explained Variance</th>\n",
+       "      <th>Sports</th>\n",
+       "      <th>SUV</th>\n",
+       "      <th>Wagon</th>\n",
+       "      <th>Minivan</th>\n",
+       "      <th>Pickup</th>\n",
+       "      <th>AWD</th>\n",
+       "      <th>RWD</th>\n",
+       "      <th>Retail</th>\n",
+       "      <th>Dealer</th>\n",
+       "      <th>Engine</th>\n",
+       "      <th>Cylinders</th>\n",
+       "      <th>Horsepower</th>\n",
+       "      <th>CityMPG</th>\n",
+       "      <th>HighwayMPG</th>\n",
+       "      <th>Weight</th>\n",
+       "      <th>Wheelbase</th>\n",
+       "      <th>Length</th>\n",
+       "      <th>Width</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Dimension 1</th>\n",
+       "      <td>0.4352</td>\n",
+       "      <td>-0.0343</td>\n",
+       "      <td>-0.1298</td>\n",
+       "      <td>0.0289</td>\n",
+       "      <td>-0.0481</td>\n",
+       "      <td>-0.0</td>\n",
+       "      <td>-0.0928</td>\n",
+       "      <td>-0.1175</td>\n",
+       "      <td>-0.2592</td>\n",
+       "      <td>-0.2576</td>\n",
+       "      <td>-0.3396</td>\n",
+       "      <td>-0.3263</td>\n",
+       "      <td>-0.3118</td>\n",
+       "      <td>0.3063</td>\n",
+       "      <td>0.3061</td>\n",
+       "      <td>-0.3317</td>\n",
+       "      <td>-0.2546</td>\n",
+       "      <td>-0.2414</td>\n",
+       "      <td>-0.2886</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Dimension 2</th>\n",
+       "      <td>0.1667</td>\n",
+       "      <td>0.4420</td>\n",
+       "      <td>-0.2261</td>\n",
+       "      <td>-0.0106</td>\n",
+       "      <td>-0.2074</td>\n",
+       "      <td>-0.0</td>\n",
+       "      <td>-0.1447</td>\n",
+       "      <td>0.3751</td>\n",
+       "      <td>0.3447</td>\n",
+       "      <td>0.3453</td>\n",
+       "      <td>0.0022</td>\n",
+       "      <td>0.0799</td>\n",
+       "      <td>0.2342</td>\n",
+       "      <td>0.0169</td>\n",
+       "      <td>0.0433</td>\n",
+       "      <td>-0.1832</td>\n",
+       "      <td>-0.3066</td>\n",
+       "      <td>-0.2701</td>\n",
+       "      <td>-0.2163</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Dimension 3</th>\n",
+       "      <td>0.1034</td>\n",
+       "      <td>0.0875</td>\n",
+       "      <td>0.4898</td>\n",
+       "      <td>0.0496</td>\n",
+       "      <td>-0.2818</td>\n",
+       "      <td>-0.0</td>\n",
+       "      <td>0.5506</td>\n",
+       "      <td>-0.2416</td>\n",
+       "      <td>0.0154</td>\n",
+       "      <td>0.0132</td>\n",
+       "      <td>-0.0489</td>\n",
+       "      <td>-0.0648</td>\n",
+       "      <td>0.0040</td>\n",
+       "      <td>-0.1421</td>\n",
+       "      <td>-0.2486</td>\n",
+       "      <td>0.0851</td>\n",
+       "      <td>-0.2846</td>\n",
+       "      <td>-0.3361</td>\n",
+       "      <td>-0.1369</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             Explained Variance  Sports     SUV   Wagon  Minivan  Pickup  \\\n",
+       "Dimension 1              0.4352 -0.0343 -0.1298  0.0289  -0.0481    -0.0   \n",
+       "Dimension 2              0.1667  0.4420 -0.2261 -0.0106  -0.2074    -0.0   \n",
+       "Dimension 3              0.1034  0.0875  0.4898  0.0496  -0.2818    -0.0   \n",
+       "\n",
+       "                AWD     RWD  Retail  Dealer  Engine  Cylinders  Horsepower  \\\n",
+       "Dimension 1 -0.0928 -0.1175 -0.2592 -0.2576 -0.3396    -0.3263     -0.3118   \n",
+       "Dimension 2 -0.1447  0.3751  0.3447  0.3453  0.0022     0.0799      0.2342   \n",
+       "Dimension 3  0.5506 -0.2416  0.0154  0.0132 -0.0489    -0.0648      0.0040   \n",
+       "\n",
+       "             CityMPG  HighwayMPG  Weight  Wheelbase  Length   Width  \n",
+       "Dimension 1   0.3063      0.3061 -0.3317    -0.2546 -0.2414 -0.2886  \n",
+       "Dimension 2   0.0169      0.0433 -0.1832    -0.3066 -0.2701 -0.2163  \n",
+       "Dimension 3  -0.1421     -0.2486  0.0851    -0.2846 -0.3361 -0.1369  "
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f9752e35c50>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pca_results?\n",
+    "pca_results(df, pca)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`5.` Use the results, to match each of the variables as the value to the most appropriate key in the dictionary below.  When you are ready to check your answers, run the following cell to see if your solution matches ours!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = 'car weight'\n",
+    "b = 'sports cars'\n",
+    "c = 'gas mileage'\n",
+    "d = 0.4352\n",
+    "e = 0.3061\n",
+    "f = 0.1667\n",
+    "g = 0.7053\n",
+    "\n",
+    "solution_5_dict = {\n",
+    "    'The first component positively weights items related to': c, \n",
+    "    'The amount of variability explained by the first component is': d,\n",
+    "    'The largest weight of the second component is related to': b,\n",
+    "    'The total amount of variability explained by the first three components': g\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "That's right!  Looks like you know a lot about PCA!\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Run this cell to check if your solution matches ours.\n",
+    "t.check_question_five(solution_5_dict)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`6.` How many components need to be kept to explain at least 85% of the variability in the original dataset?  When you think you have the answer, store it in the variable `num_comps`.  Then run the following cell to see if your solution matches ours!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.4352 1\n",
+      "0.6019 2\n",
+      "0.7053 3\n",
+      "0.7684000000000001 4\n",
+      "0.8240000000000001 5\n",
+      "0.8682000000000001 6\n",
+      "0.8971000000000001 7\n",
+      "0.9248999999999999 8\n",
+      "0.9498 9\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f9752f99358>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f9751fcc6d8>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f975230bdd8>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f975230b588>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f9752481630>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f9752481860>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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/4EVEREREROQ4uiRPREREREQkCBVMIiIiIiIiQahgEhERERERCUIFk4iIiIiISBAqmERERERERIJQwSQiIiIiIhKECiYREREREZEgVDCJiIiIiIgEoYJJREREREQkCBVMIiIiIiIiQahgEhERERERCUIFk4iIiIiISBAqmERERERERIJQwSQiIiIiIhJE5XAHUNJq1arloqOjwx2GiIiIiIicwVasWLHbOVf7VO3KXcEUHR3N8uXLwx2GiIiIiIicwcxsc1Ha6ZI8ERERERGRIFQwiYiIiIiIBKGCSUREREREJIhy9xmmwhw+fJitW7dy4MCBcIciPmeffTb16tWjSpUq4Q5FRERERCSoClEwbd26lfPOO4/o6GjMLNzhVHjOOfbs2cPWrVtp2LBhuMMREREREQmqQlySd+DAAWrWrKli6QxhZtSsWVMjfiIiIiJyxqsQBROgYukMo3yIiIiISFlQYQqmM8FTTz1Fq1atiIuLw+PxsGTJkmL3uWjRIjIyMkogOhEREREROV6F+AzT8aJHv1ui/eWM+80p22RmZjJ//nxWrlxJ1apV2b17N4cOHSrW8x45coRFixZRrVo1kpKSitWXiIiIiIicqEIWTOGwfft2atWqRdWqVQGoVasWANHR0dx4440sXLgQgDfeeIPLLruMzZs3M3ToUHbt2kXt2rV59dVXadCgAUOGDKFGjRqsWrWKGjVq8PnnnxMREcHrr7/OCy+8wPfff8/jjz9OREQEUVFRpKenh+2cRURERETKOl2SFyLdunVjy5YtNG3alLvvvptPP/3Uv6969eosXbqU4cOHc//99wMwfPhwbr31VlavXs2gQYO49957/e2/+eYbPvroI/71r38xbNgwfve735GVlUWHDh144okn+OCDD/jyyy+ZN29eyM9TRERERKQ8UcEUItWqVWPFihVMnjyZ2rVrc+ONNzJ16lQABg4c6P+amZkJeC/hu+mmmwC45ZZbWLx4sb+vfv36ERERUejzJCcnM2TIEF555RXy8vJK8YxERERERMo/XZIXQhEREaSkpJCSkkJsbCzTpk0DCs4YF2z2uMDt5557btDnmDRpEkuWLOHdd9/F4/GQlZVFzZo1S+gMREREREQqFo0whcj69evZsGGDfz0rK4tLL70UgJkzZ/q/JiYmApCUlERaWhoA06dP58orryy03/POO4/9+/f71zdu3Ei7du144oknqFWrFlu2bCmV8xERERERqQg0whQiubm5jBgxgr1791K5cmUuu+wyJk+ezPz58zl48CDt2rXj6NGjzJgxA4Dx48czdOhQnnnmGf+kD4Xp1asXffv2Ze7cubzwwgs899xzbNiwAeccXbp0IT4+PpSnKSIiIiJSrphzLtwxlKiEhAS3fPnyAtvWrl1LixYtwhTRyUVHR7N8+XL/rHkVyZmcFxEREREp38xshXMu4VTtdEmeiIiIiIhIELokL8xycnLCHYKIiIiIiAShgklERM4YsdNi/ctrBq8JYyQiIiJeuiRPREREREQkCBVMIiIiIiIiQahgEhERERERCUIFUwg99dRTtGrViri4ODweD0uWLCE6Oprdu3f72yxatIiePXuSk5NDvXr1OHr0aIE+PB4PS5cuDXXoIiIiIiIVUsWc9GFsVAn3t++UTTIzM5k/fz4rV66katWq7N69m0OHDgVtHx0dTf369fnss8/o1KkTAOvWrWP//v1cccUVJRa6iIiIiIgEpxGmENm+fTu1atWiatWqANSqVYu6deue9JiBAweSlpbmX09LS2PgwIGlGqeIiIiIiByjgilEunXrxpYtW2jatCl33303n3766SmP6d+/P3PmzOHIkSMAzJw5kwEDBpR2qCIiIiIi4qOCKUSqVavGihUrmDx5MrVr1+bGG29k6tSpmNkJbfO3XXTRRbRq1YqPP/6YrKwsqlSpQkxMTKhDFxERERGpsCrmZ5jCJCIigpSUFFJSUoiNjWXatGnUrFmTH3/8kVq1agHwww8/+Jfh2GV5F154oS7HExEREREJMY0whcj69evZsGGDfz0rK4tLL72UlJQUXnvtNQDy8vJ4/fXX6dy5s7/dDTfcwHvvvafL8UREREREwkAjTCGSm5vLiBEj2Lt3L5UrV+ayyy5j8uTJVKlShbvuuov4+Hicc/To0YObb77Zf9z5559P+/bt2bFjBw0bNgzjGYiIiIiIVDwVs2AqwjTgJa1t27ZkZGQUuu+NN9446bFz584tjZBEREREROQUdEmeiIiIiIhIECqYREREREREglDBJCIiIiIiEoQKJhERERERkSBUMImIiIiIiAShgklERERERCSIsBZMZtbDzNab2bdmNrqQ/Q3MbKGZrTKz1WZ2bTjiLAm/+93veP755/3r3bt35/bbb/evP/DAA/z1r38NR2giIiIiIhJE2O7DZGYRwESgK7AVWGZm85xzXwc0+wPwpnPuJTNrCbwHRBf3uWOnxRa3iwLWDF5zyjZJSUm89dZb3H///Rw9epTdu3fz008/+fdnZGQUKKhERERERCT8wjnCdAXwrXNuk3PuEJAGXHdcGwdU9y1HAf8JYXwlKjk52X/j2q+++oqYmBjOO+88fvzxRw4ePMjatWtp0aIFXbp0oU2bNsTGxha4Ye2TTz5J8+bN6dq1KwMHDuTZZ58FICsri/bt2xMXF0efPn348ccfAUhJSWHUqFFcccUVNG3alM8++yz0Jy0iIiIiUsaFs2C6BNgSsL7Vty3QWOBmM9uKd3RpRGhCK3l169alcuXKfPfdd2RkZJCYmEi7du3IzMxk+fLlxMXFcc455zB79mxWrlzJwoULeeCBB3DOsXz5cv71r3+xatUq3n77bZYvX+7v99Zbb+XPf/4zq1evJjY2lscff9y/78iRIyxdupTnn3++wHYRERERESmasF2SB1gh29xx6wOBqc65v5hZIvCamcU4544W6MjsDuAOgAYNGpRKsCUhf5QpIyODkSNHsm3bNjIyMoiKiiIpKQnnHI888gjp6elUqlSJbdu2sWPHDhYvXsx1111HZGQkAL169QJg37597N27l06dOgEwePBg+vXr53++66+/HoC2bduSk5MT2pMVERERESkHwjnCtBWoH7BejxMvubsNeBPAOZcJnA3UOr4j59xk51yCcy6hdu3apRRu8SUlJZGRkcGaNWuIiYmhffv2ZGZmkpGRQXJyMtOnT2fXrl2sWLGCrKwsLrzwQg4cOIBzx9eRRVO1alUAIiIiOHLkSEmeioiIiIhIhRDOgmkZ0MTMGprZWcAAYN5xbb4DugCYWQu8BdOukEZZgpKTk5k/fz41atQgIiKCGjVqsHfvXjIzM0lMTGTfvn3UqVOHKlWqsHDhQjZv3gzAlVdeyTvvvMOBAwfIzc3l3XffBSAqKooLLrjA//mk1157zT/aJCIiIiIixRe2S/Kcc0fMbDjwARABTHHOfWVmTwDLnXPzgAeAV8zsd3gv1xviTne45QwQGxvL7t27uemmmwpsy83NpVatWgwaNIhevXqRkJCAx+OhefPmAFx++eWkpqYSHx/PpZdeSkJCAlFRUQBMmzaNYcOG8fPPP9OoUSNeffXVsJybiIiIiEh5ZGW4/ihUQkKCC5wUAfDPQFeW5ebmUq1aNX7++Wc6duzI5MmTadOmTbjDKpbykBcRKVmBt30oyi0bRERETpeZrXDOJZyqXTgnfZBf4Y477uDrr7/mwIEDDB48uMwXSyIiIiIiZYEKpjLijTfeCHcIIiIiIiIVTjgnfRARERERETmjqWASEREREREJQgWTiIiIiIhIECqYREREREREglDBFCJmxi233OJfP3LkCLVr16Znz54AzJs3j3Hjxp20j//85z/07du3VOMUEREREZFjKuQseWubl+y9f1qsW3vKNueeey7Z2dn88ssvREZG8uGHH3LJJZf496emppKamnrSPurWrcusWbOKHa+IiEhpC/xdW5TfkyIiZyqNMIXQNddcw7vvvgvAjBkzGDhwoH/f1KlTGT58OABDhgzh3nvvJSkpiUaNGvmLpJycHGJiYgBo164dX331lf/4lJQUVqxYwdKlS0lKSqJ169YkJSWxfv16f//XX389PXr0oEmTJjz00EMhOWcRERERkbJMBVMIDRgwgLS0NA4cOMDq1atp165d0Lbbt29n8eLFzJ8/n9GjRxfa15tvvulv+5///Ie2bdvSvHlz0tPTWbVqFU888QSPPPKI/5isrCxmzpzJmjVrmDlzJlu2bCn5kxQRERERKUcq5CV54RIXF0dOTg4zZszg2muvPWnb3r17U6lSJVq2bMmOHTtO2N+/f3+6du3K448/zptvvkm/fv0A2LdvH4MHD2bDhg2YGYcPH/Yf06VLF6KiogBo2bIlmzdvpn79+iV4hiIiIiIi5YtGmEIsNTWV3//+9wUuxytM1apV/cvOuRP2X3LJJdSsWZPVq1czc+ZMBgwYAMD/+3//j86dO5Odnc0777zDgQMHCu0zIiKCI0eOFPd0RERERETKNY0whdjQoUOJiooiNjaWRYsWFauvAQMG8PTTT7Nv3z5iY2MB7whT/mQSU6dOLWa0IiIiIiIVm0aYQqxevXrcd999JdJX3759SUtLo3///v5tDz30EA8//DDJycnk5eWVyPOIiIiIiFRUVtjlXmVZQkKCW758eYFta9eupUWLkp1KXIpPeRGR48VOi/Uvrxm8JoyRSHFpWnEROdOZ2QrnXMKp2mmESUREREREJAgVTCIiIiIiIkGoYBIREREREQlCBZOIiIiIiEgQKphERERERESCUMEkIiIiIiIShAqmEImIiMDj8RATE0O/fv34+eefAUhKSjrpcSkpKRw/TbqIiIiIiIRG5XAHEA4Th31Sov3dM+mqU7aJjIwkKysLgEGDBjFp0iRGjhxJRkZGicYiIiIiIiIlRyNMYdChQwe+/fZbAKpVq+bf/vTTTxMbG0t8fDyjR48ucMzRo0cZPHgwf/jDH044btasWQwZMgSAIUOGMGzYMDp06EDTpk2ZP39+KZ+NiIiIiEj5VSFHmMLpyJEjvP/++/To0aPA9vfff585c+awZMkSzjnnHH744YcCxwwaNIiYmBjGjBlzyufIycnh008/ZePGjXTu3Jlvv/2Ws88+u8TPRURERESkvNMIU4j88ssveDweEhISaNCgAbfddluB/R999BG//e1vOeeccwCoUaOGf9+dd95Z5GIJoH///lSqVIkmTZrQqFEj1q1bV3InIiIiIiJSgWiEKUQCP8NUGOccZlbovqSkJBYuXMgDDzzgHykKbHvgwIEC7Y/vJ1i/IiIiIiJychphOkN069aNKVOm+GfPC7wk77bbbuPaa6+lX79+HDlyBIALL7yQtWvXcvToUWbPnl2gr7feeoujR4+yceNGNm3aRLNmzUJ3IiIiIiIi5YgKpjNEjx49SE1NJSEhAY/Hw7PPPltg/8iRI2nTpg233HILR48eZdy4cfTs2ZOrrrqKiy++uEDbZs2a0alTJ6655homTZqkzy+JiIiIiJwmc86FO4YSlZCQ4I6/b9HatWtp0aJFmCIKrSFDhtCzZ0/69u0b7lBOqSLlRUSKJnZarH95zeA1YYxEimtt82Pv7y3WrQ1jJCIihTOzFc65hFO10wiTiIiIiIhIEJr0oZyZOnVquEMQERERESk3NMIkIiIiIiIShAomERERERGRIFQwiYiIiIiIBKGCSUREREREJAgVTCE2e/ZszIx169YB0KdPH+bMmePf36xZM/74xz/612+44QbefvttFi1aRFRUFK1bt6ZZs2Z07NiR+fPnhzx+EREREZGKpELOkveXG3uWaH8PzCx64TJjxgyuvPJK0tLSGDt2LElJSWRkZNC7d2/27NlDtWrVyMzM9LfPzMxk4sSJrFu3jg4dOviLpKysLHr37k1kZCRdunQp0fMREREREREvjTCFUG5uLp9//jn/+Mc/SEtLAyA5OZmMjAwAMjIy6NmzJ7t27cI5x7///W8iIyO56KKLTujL4/Hw6KOPMmHChJCeg4iIiIhIRaKCKYTmzJlDjx49aNq0KTVq1GDlypW0bduW7OxsDh06REZGBomJiTRr1oy1a9eSkZFBcnJy0P6rldQWAAAgAElEQVTatGnjv7RPRERERERKngqmEJoxYwYDBgwAYMCAAcyYMYOqVavSqlUrVq5cyRdffEG7du1ITEwkIyODjIwMkpKSgvbnnAtV6CIiIiIiFVKF/AxTOOzZs4dPPvmE7OxszIy8vDzMjKeffpqkpCTS09PZv38/F1xwAe3bt2fChAmsWrWKYcOGBe1z1apVtGjRIoRnISIiIiJSsWiEKURmzZrFrbfeyubNm8nJyWHLli00bNiQxYsXk5yczMsvv0x8fDwAcXFxfPHFF3z33Xe0atWq0P5Wr17Nk08+yT333BPK0xARERERqVBUMIXIjBkz6NOnT4FtN9xwA2+88QZJSUls2rSJxMREACpXrkydOnVISEigUqVjKfrss8/804rfc889jB8/XjPkiYiIiIiUogp5Sd6vmQa8pCxatOiEbffee69/+fjPIx3fPiUlhX379pVGaCIiIiIiEoRGmERERERERIJQwSQiIiIiIhKECiYREREREZEgVDCJiIiIiIgEoYJJREREREQkCBVMIiIiIiIiQahgCpGIiAg8Hg8xMTH06tWLvXv3AtCnTx/mzJnjb9esWTP++Mc/+tdvuOEG3n77bRYtWkRUVJT/PkwdO3Zk/vzQT48uIiIiIlKRhPU+TGbWA/gbEAH83Tk3rpA2/YGxgAO+dM7dVNzn3Tr6s+J2UUC9cR1O2SYyMpKsrCwABg8ezMSJExkzZgxJSUlkZGTQu3dv9uzZQ7Vq1cjMzPQfl5mZycSJE1m3bh0dOnTwF0lZWVn07t2byMhI3bxWRERERKSUhG2EycwigInANUBLYKCZtTyuTRPgYSDZOdcKuD/kgZaCxMREtm3bBkBycjIZGRkAZGRk0LNnT3bt2oVzjn//+99ERkZy0UUXndCHx+Ph0UcfZcKECSGNXURERESkIgnnJXlXAN865zY55w4BacB1x7X5H2Cic+5HAOfczhDHWOLy8vL4+OOPSU1NBaBt27ZkZ2dz6NAhMjIySExMpFmzZqxdu5aMjAySk5OD9tWmTRvWrVsXqtBFRERERCqccBZMlwBbAta3+rYFago0NbPPzewL3yV8ZdIvv/yCx+OhZs2a/PDDD3Tt2hWAqlWr0qpVK1auXMkXX3xBu3btSExMJCMjg4yMDJKSkoL26ZwLVfgiIiIiIhVSOAsmK2Tb8RVAZaAJkAIMBP5uZuef0JHZHWa23MyW79q1q8QDLQn5n2HavHkzhw4dYuLEif59SUlJpKens3//fi644ALat2/vL5hONsK0atUqWrRoEYrwRUREREQqpHAWTFuB+gHr9YD/FNJmrnPusHPu38B6vAVUAc65yc65BOdcQu3atUst4JIQFRXF+PHjefbZZzl8+DDg/RzTyy+/THx8PABxcXF88cUXfPfdd7Rq1arQflavXs2TTz7JPffcE7LYRUREREQqmnAWTMuAJmbW0MzOAgYA845rMwfoDGBmtfBeorcppFGWgtatWxMfH09aWhrgHWHatGkTiYmJAFSuXJk6deqQkJBApUrHUvTZZ5/5pxW/5557GD9+vGbIExEREREpRWGbVtw5d8TMhgMf4J1WfIpz7iszewJY7pyb59vXzcy+BvKAB51ze4r73EWZBryk5ebmFlh/5513/Mt16tQ54fNIixYtKrCekpLCvn37Si0+ERERERE5UVjvw+Scew9477htjwYsO2Ck7yEiIiIiIhJS4bwkT0RERERE5IymgklERERERCQIFUwiIiIiIiJBqGASEREREREJQgWTiIiIiIhIECqYQiQiIgKPx0NMTAy9evVi7969J22/d+9eXnzxxSL1nZSUBEBOTg4xMTHFjlVERERERLzCOq14uIwdOzbk/UVGRpKVlQXA4MGDmThxImPGjAnaPr9guvvuu0/Zd0ZGRpFjFRERERGRotMIUxgkJiaybds2//ozzzzD5ZdfTlxcHI899hgAo0ePZuPGjXg8Hh588EFyc3Pp0qULbdq0ITY2lrlz5/qPr1atWsjPQURERESkIqiQI0zhlJeXx8cff8xtt90GwIIFC9iwYQNLly7FOUdqairp6emMGzeO7Oxs/6jUkSNHmD17NtWrV2f37t20b9+e1NRUzCycpyMiIiIiUq6pYAqRX375BY/HQ05ODm3btqVr166At2BasGABrVu3BiA3N5cNGzbQoEGDAsc753jkkUdIT0+nUqVKbNu2jR07dnDRRReF/FxERERERCoKFUwhkv8Zpn379tGzZ08mTpzIvffei3OOhx9+mDvvvLNA+5ycnALr06dPZ9euXaxYsYIqVaoQHR3NgQMHQngGIuXLX27s6V9+YOb8MEYiIiIiZzJ9hinEoqKiGD9+PM8++yyHDx+me/fuTJkyhdzcXAC2bdvGzp07Oe+889i/f7//uH379lGnTh2qVKnCwoUL2bx5c7hOQURERESkwtAIUxi0bt2a+Ph40tLSuOWWW1i7di2JiYmAdwKH119/ncaNG5OcnExMTAzXXHMNo0aNolevXiQkJODxeGjevHmYz0JEREREpPyrkAVTSU8rXhT5I0j53nnnHf/yfffdx3333XfCMW+88UaB9czMzJP2HR0dTXZ2dnFDFRERERERH12SJyIiIiIiEoQKJhERERERkSBUMImIiIiIiAShgklERERERCQIFUwiIiIiIiJBqGASEREREREJokJOKx4OERERxMbGcvjwYSpXrszgwYO5//77qVTp9GrWatWqnTBVuYiIiIiUX9Gj3/Uv54z7TRgjqVgqZMH08SeNS7S/LldtPGWbyMhIsrKyANi5cyc33XQT+/bt4/HHHy/RWArjnMM5d9rFmYiIiIhIRaW/oMOgTp06TJ48mQkTJuCcIy8vjwcffJDLL7+cuLg4Xn75ZcB7Q9ouXbrQpk0bYmNjmTt3bqH9PfPMM/5jH3vsMQBycnJo0aIFd999N23atGHLli0hOz8RERERkfKiQo4wnQkaNWrE0aNH2blzJ3PnziUqKoply5Zx8OBBkpOT6datG/Xr12f27NlUr16d3bt30759e1JTUzEzfz8LFixgw4YNLF26FOccqamppKen06BBA9avX8+rr77Kiy++GMYzFREREREpu1QwhZFzDvAWPatXr2bWrFkA7Nu3jw0bNlCvXj0eeeQR0tPTqVSpEtu2bWPHjh1cdNFF/j4WLFjAggULaN26NeAdldqwYQMNGjTg0ksvpX379qE/MRERERGRckIFU5hs2rSJiIgI6tSpg3OOF154ge7duxdoM3XqVHbt2sWKFSuoUqUK0dHRHDhwoEAb5xwPP/wwd955Z4HtOTk5nHvuuaV+HiIiIiIi5Zk+wxQGu3btYtiwYQwfPhwzo3v37rz00kscPnwYgG+++Yb//ve/7Nu3jzp16lClShUWLlzI5s2bT+ire/fuTJkyxT9j3rZt29i5c2dIz0dEREREpLzSCFOI/PLLL3g8Hv+04rfccgsjR44E4PbbbycnJ4c2bdrgnKN27drMmTOHQYMG0atXLxISEvB4PDRv3vyEfrt168batWtJTEwEvNONv/7660RERIT0/EREREREyqMKWTAVZRrwkpaXlxd0X6VKlfjTn/7En/70pxP2ZWZmFnpM4D2Y7rvvPu67774T2mRnZ59GpCIiIiIikq9CFkwiUg6NjQpY3he+OERERKRc0WeYREREREREglDBJCIiIiIiEoQKJhERERERkSBUMImIiIiIiAShgklERERERCQIFUwhEhERgcfj8T/GjRt32n0lJSWVYGQiIiIiIhJMhZxW/KKFWSXa3/edPadsExkZSVZWyTxvRkZGifQjIiIiIiInpxGmMIuOjuaxxx6jTZs2xMbGsm7dOgB27dpF165dadOmDXfeeSeXXnopu3fvBqBatWoALFq0iJSUFPr27Uvz5s0ZNGgQzjkAVqxYQadOnWjbti3du3dn+/bt4TlBEREREZEyTAVTiPzyyy8FLsmbOXOmf1+tWrVYuXIld911F88++ywAjz/+OFdddRUrV66kT58+fPfdd4X2u2rVKp5//nm+/vprNm3axOeff87hw4cZMWIEs2bNYsWKFQwdOpQxY8aE5DxFRERERMqTCnlJXjic7JK866+/HoC2bdvy9ttvA7B48WJmz54NQI8ePbjgggsKPfaKK66gXr16AHg8HnJycjj//PPJzs6ma9euAOTl5XHxxReX6PmIiIiIiFQEKpjOAFWrVgW8E0McOXIEwH9pXVGPDTzeOUerVq3IzMws+WBFRERERCoQXZJ3hrryyit58803AViwYAE//vhjkY9t1qwZu3bt8hdMhw8f5quvviqVOEVEREREyjMVTCFy/GeYRo8efdL2jz32GAsWLKBNmza8//77XHzxxZx33nlFeq6zzjqLWbNmMWrUKOLj4/F4PJpZT0RERETkNFTIS/KKMg14ScvLyyt0e05Ojn85ISGBRYsWARAVFcUHH3xA5cqVyczMZOHChf7L73JzcwFISUkhJSXFf/yECRP8yx6Ph/T09JI9iXIoevS7/uWccb8JYyQiIiIiciaqkAVTWfDdd9/Rv39/jh49yllnncUrr7wS7pBERERERErU2LFjC10+k6hgOkM1adKEVatWhTsMEREREZEKTZ9hEhERERERCUIFk4iIiIiISBAqmERERERERIJQwSQiIiIiIhKECqYQ+v777xkwYACNGzemZcuWXHvttXzzzTeFtl20aBE9e/YEYN68eYwbN+5XPdeQIUOYNWtWsWMWEREREanIKuQseYH33ikJRbl/j3OOPn36MHjwYNLS0gDIyspix44dNG3a9KTHpqamkpqaWiKxBnPkyBEqV66QPw4iIiIiIkGFdYTJzHqY2Xoz+9bMRp+kXV8zc2aWEMr4StLChQupUqUKw4YN82/zeDxMnjyZuXPn+rcNGjSIefPmFTh26tSpDB8+HPCOHN17770kJSXRqFEj/yiSc47hw4fTsmVLfvOb37Bz507/8StWrKBTp060bduW7t27s337dsB749tHHnmETp068be//Y233nqLmJgY4uPj6dixY6l9L0REREREyoqwDSmYWQQwEegKbAWWmdk859zXx7U7D7gXWBL6KEtOdnY2bdu2PWH77bffznPPPcd1113Hvn37yMjIYNq0aSxevDhoX9u3b2fx4sWsW7eO1NRU+vbty+zZs1m/fj1r1qxhx44dtGzZkqFDh3L48GFGjBjB3LlzqV27NjNnzmTMmDFMmTIFgL179/Lpp58CEBsbywcffMAll1zC3r17S+cbISIiIiLlRuy0WP/ymsFrwhhJ6QnnNVhXAN865zYBmFkacB3w9XHtngSeBn4f2vBCo1OnTtxzzz3s3LmTt99+mxtuuOGUl8b17t2bSpUq0bJlS3bs2AFAeno6AwcOJCIigrp163LVVVcBsH79erKzs+natSsAeXl5XHzxxf6+brzxRv9ycnIyQ4YMoX///lx//fUlfaoiIiJSAXz8SWP/cperNoYxEpGSEc6C6RJgS8D6VqBdYAMzaw3Ud87NN7MyXTC1atUq6CQMt9xyC9OnTyctLc0/8nMyVatW9S875/zLZnZCW+ccrVq1IjMzs9C+zj33XP/ypEmTWLJkCe+++y4ej4esrCxq1qx5ynhERESkYhs7dqx/uYOu6pdyJpyfYTrxr3vw//VvZpWA54AHTtmR2R1mttzMlu/atasEQyw5V111FQcPHuSVV17xb1u2bBmffvopQ4YM4fnnnwe8hdXp6NixI2lpaeTl5bF9+3YWLlwIQLNmzdi1a5e/YDp8+DBfffVVoX1s3LiRdu3a8cQTT1CrVi22bNlSaDsRERERkYoinAXTVqB+wHo94D8B6+cBMcAiM8sB2gPzCpv4wTk32TmX4JxLqF27dimGfPrMjNmzZ/Phhx/SuHFjWrVqxdixY6lbty4XXnghLVq04Le//e1p99+nTx+aNGlCbGwsd911F506dQLgrLPOYtasWYwaNYr4+Hg8Hg8ZGRmF9vHggw8SGxtLTEwMHTt2JD4+/rTjEREREREpD8J5Sd4yoImZNQS2AQOAm/J3Ouf2AbXy181sEfB759zy4j5xUaYBLw1169blzTffPGH7zz//zIYNGxg4cKB/W0pKCikpKYB3ZrwhQ4YA3hnzAuXm5gLegmzChAmFPq/H4yE9Pf2E7YsWLSqw/vbbbxfxTEREREREKoawjTA5544Aw4EPgLXAm865r8zsCTMr3ZsOnUE++ugjmjdvzogRI4iKigp3OCIiIiIiEiCsdyp1zr0HvHfctkeDtE0JRUyhdvXVV/Pdd9+FOwwRERERESlEWG9cKyIiIiIiciZTwSQiIiIiIhKECiYREREREZEgwvoZJpHyZOvoz/zL9cZ1CGMkIiIiIlJSNMIUItWqVSuwPnXqVIYPHx6maEREREREpCgq5gjT2BKevnvsvpLtrxBHjhyhcuUzP11lJU4RERERkaLQCNMZYPPmzXTp0oW4uDi6dOnin2Z8yJAhjBw5ks6dOzNq1Cg+/fRTPB4PHo+H1q1bs3//fgCeeeYZLr/8cuLi4njssccAyMnJoXnz5gwePJi4uDj69u3Lzz//DMDHH39M69atiY2NZejQoRw8eJClS5dy/fXXAzB37lwiIyM5dOgQBw4coFGjRgBs3LiRHj160LZtWzp06MC6desKjVNEREREpLzQUECI/PLLL3g8Hv/6Dz/8QGqq9/68w4cP59Zbb2Xw4MFMmTKFe++9lzlz5gDwzTff8NFHHxEREUGvXr2YOHEiycnJ5ObmcvbZZ7NgwQI2bNjA0qVLcc6RmppKeno6DRo0YP369fzjH/8gOTmZoUOH8uKLLzJ8+HCGDBnCxx9/TNOmTbn11lt56aWXGD58OKtWrQLgs88+IyYmhmXLlnHkyBHatWsHwB133MGkSZNo0qQJS5Ys4e677+aTTz45IU4RERERkfLilCNMZnafmVU3r3+Y2Uoz6xaK4MqTyMhIsrKy/I8nnnjCvy8zM5ObbroJgFtuuYXFixf79/Xr189fhCQnJzNy5EjGjx/P3r17qVy5MgsWLGDBggW0bt2aNm3asG7dOjZs2ABA/fr1SU5OBuDmm29m8eLFrF+/noYNG9K0aVMABg8eTHp6OpUrV+ayyy5j7dq1LF26lJEjR5Kens5nn31Ghw4dyM3NJSMjg379+uHxeLjzzjvZvn17oXGKiIiIiJQXRRlhGuqc+5uZdQdqA78FXgUWlGpkFZiZ+ZfPPfdc//Lo0aP5zW9+w3vvvUf79u356KOPcM7x8MMPc+eddxboIycnp0A/+f0654I+b4cOHXj//fepUqUKV199NUOGDCEvL49nn32Wo0ePcv7555OVlVXosYFxioiIiIiUF0X5DFP+X93XAq86574M2CYlICkpibS0NACmT5/OlVdeWWi7jRs3Ehsby6hRo0hISGDdunV0796dKVOmkJubC8C2bdvYuXMnAN999x2ZmZkAzJgxgyuvvJLmzZuTk5PDt99+C8Brr71Gp06dAOjYsSPPP/88iYmJ1K5dmz179rBu3TpatWpF9erVadiwIW+99RYAzjm+/PLL0vumiIiIyBnnLzf29D9EKoqiFEwrzGwB3oLpAzM7DzhaumFVLOPHj+fVV18lLi6O1157jb/97W+Ftnv++eeJiYkhPj6eyMhIrrnmGrp168ZNN91EYmIisbGx9O3b1z8ZRIsWLZg2bRpxcXH88MMP3HXXXZx99tm8+uqr9OvXj9jYWCpVqsSwYcMAaNeuHTt27KBjx44AxMXFERcX5x+pmj59Ov/4xz+Ij4+nVatWzJ07NwTfHRERERGR8CnKJXm3AR5gk3PuZzOrifeyvLIrBNOAHy9/BCjfkCFDGDJkCADR0dH+yRMCTZ06tcD6Cy+8UGjf9913H/fdd1+BbTk5OVSqVIlJkyad0L5Lly7+CR4CRUZGcvDgQf/65MmTC+xv2LAh//d//3fKOAXGjh3rX+7Q8TX/cperNoYhGhGR0IidFutffjOMcYiIlKSijDB96Jxb6ZzbC+Cc2wM8V7phiYiIiIiIhF/QESYzOxs4B6hlZhdw7HNL1YG6IYhNiiE6Oprs7OxwhyEiIiIiUqad7JK8O4H78RZHKzhWMP0ETCzluERERERERMIuaMHknPsb8DczG+GcK/zDMyIiIiIixRT4+bc1g9eEMRKRE51y0gfn3AtmlgREB7Z3zv2zFOMSERERkQpobfMW/uUW69aGMRIRr1MWTGb2GtAYyALyfJsdoIJJRERERETKtaLMkpcAJDvn7nbOjfA97i3twMqj77//ngEDBtC4cWNatmzJtddeS3p6On379gUgKyuL995775T9jB07FjPz33wW4LnnnsPMWL58OeCd9CE2Npb4+Hi6devG999/D3inN7/rrrto3LgxrVu3pm3btrzyyiulcLYiIiIiImVfUe7DlA1cBGwv5VhCJvA62ZJQlGttnXP06dOHwYMHk5aWBngLpP379zNr1iz/+vLly7n22mtP2V9sbCxpaWn84Q9/AGDWrFm0bNmyQJuFCxdSq1YtHnnkEf70pz8xfvx4br/9dho1asSGDRuoVKkSu3btYsqUKb/2lEVEREREKoSgI0xm9o6ZzQNqAV+b2QdmNi//EboQy4eFCxdSpUoVhg0b5t/m8XioX78+MTExHDp0iEcffZSZM2fi8XiYOXMmTZo0YdeuXQAcPXqUyy67jN27dwPQu3dv5s6dC8CmTZuIioqidu3ahT53x44d+fbbb9m4cSNLly7lj3/8I5UqeVNfu3ZtRo0aVZqnLiIiIiIlbWzUsccZYm3zFv5HeXKyEaZnQxZFBZCdnU3btm2D7j/rrLN44oknWL58ORMmTABg3bp1TJ8+nfvvv5+PPvqI+Ph4atWqBUD16tWpX78+2dnZzJ07lxtvvJFXX3210L7nz59PbGwsX331FfHx8f5iSURERERETi7oX87OuU9P9ghlkBXV0KFD+ec/vXNrTJkyhd/+9rcF9g8YMIC0tDTmzJlDnz59Tji+c+fOeDwefvrpJx5++OET9j/11FN4PB7q1tV9iEVERERECnPKoQYz229mPx332GJms82sUSiCLA9atWrFihUrftUx9evX58ILL+STTz5hyZIlXHPNNQX29+rVi9dee40GDRpQvXr1AvsOHz3MS7NeYvpH03n5oYeounUrjSpX5ssvv+To0aMAjBkzhqysLH766afinZyIiIiISDlVlGuz/go8CFwC1AN+D7wCpAGaLaCIrrrqKg4ePFhgRrply5axefNm//p5553H/v37Cxx3++23c/PNN9O/f38iIiIK7IuMjOTPf/4zY8aMKVIMjRs0ICEhgT/84Q/k5XlniD9w4ADOudM9LRERERGRcq0oBVMP59zLzrn9zrmfnHOTgWudczOBC0o5vnLDzJg9ezYffvghjRs3plWrVowdO7bA5XCdO3fm66+/9k/6AJCamkpubu4Jl+PlGzBgAG3atClyHH//+9/Zs2cPl112GW3btuXqq6/mz3/+c/FOTkREKpTo0e/6HyIi5V1RphU/amb9gVm+9b4B+8rk0ERRpgEvDXXr1uXNN988YXt2djYANWrUYNmyZQX2ffnll8THx9O8eXP/trFjxxba/6JFi/zLC1YuKLRN9erVefnll39l5CIiIiIiFVNRRpgGAbcAO4EdvuWbzSwSGF6KsVV448aN44YbbuB///d/wx2KiIiIiEiFdMoRJufcJqBXkN2LSzYcCTR69GhGjx4d7jBERERERCqsoAWTmT3knHvazF6gkEvvnHP3lmpkIiIiIiIiYXayEaa1vq/LQxGIiIiIiIjImSZoweSce8f3dRqAmZ3rnPtvqAITEREREREJt6LcuDbRzL7GN+JkZvFm9mKpRyYiIiIiIhJmRZkl73mgO7AHwDn3JdCxNIMqj6pVq1ZgferUqQwf7p1kcNKkSfzzn/886fGB7UtbSkoKDRo0KHBD2969e/vPIScnh8jISDweDy1btmTYsGEcPXoUgA0bNtCzZ08aN25M27Zt6dy5M+np6SGJW0RERESkpBXlPkw49//bu/fwqKpz8ePfZZCLFaKIVBEU9Ee9EGIQBBOEegWrVouXYsEW66GU6qn3Wqm9pJejaMWHtvqUY73gqfSIAlaLnmpFLWpiEWoKRGhRDyJ4xYrIAZHL+v2RcTqBTAiQZCcz38/zzJO196xZ+92zcntnrb12fCOEkLlrS9OE0zyWHHFko7Z35NIlO65Uj/HjxzdSJI1nn3324fnnn+f4449nzZo1vPXWW7WeP+yww6iqqmLz5s2cdNJJ/P73v+f000/njDPO4JZbbuGss84Cau4xNX/+fIYONceWJElS69OQEaY3QghlQAwhtA0hXMO/FoRQIygvL+eWW24B4MUXX6S4uJjS0lK+853vUFRUlK735ptvctppp9G7d2+uvfZaAB544AGuuuoqAH7xi19w6KGHArDif1fw1TO+CsANv/41x19wAQNGjGDcuHHEGHn11Vc55phj0m0vW7aM/v37p7cvuOAC7r//fgBmzZrFOeecU2fsbdq0oaysjFdeeYVp06ZRWlqaTpYAioqKuOiii3b3LZIkSZIS0ZCEaTxwKXAQsBIoSW1rJ2zYsIGSkpL044c//GGd9b7+9a8zZcoUKisrKSgoqPVcVVUV06dPZ9GiRUyfPp033niDoUOH8uyzzwLw7LPPst9++7Fq1Spe+stLHHNcTUI0ftQonrv/fuY/9BAbNmxg9uzZHHbYYRQWFlJVVQXAPffcUyuxOfnkk5k7dy5btmzh/vvvZ+TIkXXGu379eubMmUPfvn2prq6ulYRJkiRJrV3WhCmEsC9AjHF1jHF0jPGzMcauMcYLY4zvN1+IuaFDhw5UVVWlHz/5yU+2q7NmzRo++ugjysrKABg1aqtCLDsAACAASURBVFSt508++WQKCwtp3749Rx11FK+//joHHHAA69at46OPPuKNN95g1KhRzJ07lwUvLKD/cTUjRnPnzWPoqFEcO2IETz31FNXV1QCMHTuWe+65hy1btjB9+vRaxysoKOD4449n+vTpbNiwgZ49e9aK5dVXX6WkpITBgwdzxhln8IUvfGG78xkxYgRFRUVZR6ckSZKklq6+a5j+HkJ4D6gAngcqYoz/aJ6w8lPmIgt1adeuXbpcUFDA5s2bASgtLeWee+7h8MMPZ8iQIdx99938bf7f+M5PvsPGjzdyxc9+xnPTp9P9gAO4acYMPv74YwDOPfdcfvzjH3PSSSfRv39/9ttvv1rHu+CCCxgxYgTl5eXbxfLpNUyZ+vTpU2uBh4ceeoj58+dzzTXX7NT7IEmSJLUUWUeYYoxdgRHUJEtlwKwQwjshhIdDCNc2V4D5ZN9996Vjx4688MILAOlriHZk6NCh3HLLLQwdOpR+/frx9NNP07ZtWzp26sjGjRsB2G+ffVi3fj0zZsxIv659+/YMHz6cb33rW3z961/frt0hQ4YwYcIEvvKVrzQojlGjRvH888/zyCOPpPetX7++Qa+VJEmSWqJ6V8lLjSj9A5gaQjgMOB24HBgG3Nz04eWfu+66i2984xt85jOf4YQTTqCwsHCHrxkyZEj6eqaCggJ69OjB/ofsD0Cnwk5cdO65HHvOORzSrRvHHntsrdeOHj2aWbNmMWzYsO3aDSHs1OhQhw4dmD17NldddRVXXHEFn/3sZ+nYsSPf//73G9yGJEmSdk7fe/umy4vGLEowktyUNWFKrYxXBpQCPYDXgBeAC4G/Nkt0TWR3lwHfFevWrau1fdFFF6UXWcic8tanTx8WLlwIwMSJExkwYMB29QFmz56dLh922GG1pvM98cQTVK+uTm+XX3YZ5ZddBkCHjFX3AJ577jkuvvjiWgtMPPPMM/WeQ8+ePVm8eHGddY444ggee+yxOp+TJEmSWpv6RpieoyYxuhX4fYzRuVXN4NFHH+XGG29k8+bNHHLIIUydOrXJjjVixAheffVVnnrqqSY7hiRJktSa1ZcwdaNmhKkMGB9CaENNAlUJVMYYX2uG+PLOyJEjsy7h3dgeeuihZjmOJEmS1FplTZhijG8Ds1IPQgh7ARcDPwZ6AQXZXitJkiRJuaC+a5gKqbl+6dNRpn7AK8AfqFk5T1JjKc9Y3KP8w+TikCRJUi31Tcl7hZpFHiqAnwLzYowbmiUqSZIkSWoB6puSt39zBiJJkiRJLU3WG9eqcV155ZVMnjw5vT18+HDGjh2b3r766qu59dZbs76+rKxsh8fo2bMnq1ev3m7/3Bdf5IWqqp2MWJIkSVK9N67NVbePb9xltC+dctIO65SVlfHggw9yxRVXsHXrVlavXs3atWvTz1dUVNRKqLZVUVGxy/HNffFF9t5rL44rKdnlNiRJkqR85AhTMxk8eHA66amurqaoqIiOHTvywQcfsHHjRpYsWUK/fv34+c9/zrHHHktxcTE/+tGP0q/fe++9Adi6dSuXXHIJffr04cwzz+T0009nxowZ6Xq/+tWvOOaYYxgxdASvLXuNVStWcecDD/Cr3/6WQeedx7PPPtu8Jy5JkiS1YjtMmEIInwshzAkhLE5tF4cQvt/0oeWWbt260aZNG1asWEFFRQWlpaUMGjSIyspK5s+fT3FxMc888wzLli1j3rx5VFVVsWDBAubOnVurnVmzZrF8+XIWLVrEnXfeSWVlZa3nu3Tpwl//+ldGXjSSqbdP5aCDD2Lsl7/Mt7/6Vf4yYwZDhgxpztOWJEmSWrWGjDD9BpgAbAKIMS4ELmiMg4cQTgsh/D2E8EoI4bo6nr8qhPByCGFhKmk7pDGOm5RPR5k+TZhKS0vT22VlZTzxxBM88cQT9OvXj2OOOYalS5eybNmyWm0899xznH/++eyxxx4ccMABnHjiibWeP+eccwA46uijePONN5vt3CRJkqRc1JBrmPaKMc4LIWTu27y7Bw4hFAC3A6cCK4EXQwiPxBhfzqj2EjAgxrg+hPAt4GZg5O4eOyllZWVUVFSwaNEiioqK6NGjB5MmTaJTp05cfPHFPPPMM0yYMIFvfvObWduIMdZ7jHbt2gGwR8EebN68290kSZIk5bWGjDCtDiEcBkSAEMJ5wFuNcOyBwCsxxtdijJ8A9wNnZ1aIMT4dY1yf2nwB6N4Ix03M4MGDmT17Np07d6agoIDOnTuzZs0aKisrKS0tZfjw4dx9992sW7cOgFWrVvHuu+/WauP4449n5syZbN26lXfeeYdnnnlmh8ft+JnP8NH//V9TnJIkSZKU0xoywnQpcAdwRAhhFfC/wOhGOPZBwBsZ2yuBQfXU/zfgfxrhuInp27cvq1evZtSoUbX2rVu3ji5dujBs2DCWLFlCaWkpULPQw3333UfXrl3T9c8991zmzJlDUVERn/vc5xg0aBCFhYX1Hvf0z3+e0Vddxeynn+b23/zG65gkSYmZNPLMdPnq6bMTjESSGqbehCmEsAc1U+JOCSF8BtgjxvhRIx071LGvzvlmIYQLgQHA57M8Pw4YB3DwwQfv8MANWQa8KRQUFNRaShxg6tSptbYvv/xyLr/88u1e++mo0x577MEtt9zC3nvvzfvvv8/AgQPp27cvAMuXL0/XLyopYurDNW337tmTebNmAdChqKiRzkaSJEnKffUmTDHGrSGEfwceiDE29pyulUCPjO3uwHarFIQQTgGuBz4fY9yYJc47qBkFY8CAAfVf5JMDzjzzTNasWcMnn3zCD37wAw444ICkQ5IkSZJyUkOm5P0phHANMB1IJ00xxn/u5rFfBHqHEHoBq6hZeW9UZoUQQj/gP4HTYozvbt9EfmrIdUuSJEmSdl9DEqaLU18vzdgXgUN358Axxs2p0avHgQLg7hhjdQjhJ8D8GOMjwM+BvYEHU6v0rYgxnrU7x5UkSZKkhtphwhRj7NVUB48xPgY8ts2+H2aUT2mqY0uSJEnSjuwwYQohfK2u/THG/2r8cCRJkiSp5WjIlLxjM8rtgZOBvwImTJIkSZJy2g5vXBtj/HbG4xtAP6Bt04eWW6688komT56c3h4+fDhjx45Nb1999dXceuutnHnmmXW9fKfdfvPt3HP7PTXH+vrXWVBd3SjtSpIkSfmkISNM21oP9G7sQJpT5k3zGkNDbrxXVlbGgw8+yBVXXMHWrVtZvXp1rXsyVVRU8KUvfalR45IkSZK0e3Y4whRC+EMI4ZHUYzbwd+CRpg8ttwwePJiKigoAqqurKSoqomPHjnzwwQds3LiRJUuW0K9fP9atW8d5553HEUccwejRo4mx5rZSCxYs4POf/zz9+/dn+PDhvPXWWwC8+uqrnHbaafTv358hQ4awdOnSOo9//+zZnHjhhRQVFTFv3jwA5s2bR1lZGf369aOsrIy///3v6fgGDhxISUkJxcXFLFu2DID77rsvvf+b3/wmW7ZsadL3TJIkSUpaQ0aYbskobwZejzGubKJ4cla3bt1o06YNK1asoKKigtLSUlatWkVlZSWFhYUUFxfTtm1bXnrpJaqrq+nWrRuDBw/m+eefZ9CgQXz729/m4YcfZv/992f69Olcf/313H333YwbN44pU6bQu3dv/vKXv3DJJZfw1FNPbXf8/9uwgafvu48X//lPLr74YhYvXswRRxzB3LlzadOmDU8++STf+973mDlzJlOmTOHyyy9n9OjRfPLJJ2zZsoUlS5Ywffp0nn/+efbcc08uueQSpk2bxte+VueaIJIkSVJOaEjCdHqM8buZO0IIN227Tzv26ShTRUUFV111FatWraKiooLCwkLKysoAGDhwIN27dwegpKSE5cuXs88++7B48WJOPfVUALZs2cKBBx7IunXrqKio4Pzzz08fY+PGjXUe+8tf+AIAQ4cOZe3ataxZs4aPPvqIMWPGsGzZMkIIbNq0CYDS0lL+4z/+g5UrV3LOOefQu3dv5syZw4IFCzj22Jo1QDZs2EDXrl2b5o2SJEmSWoiGJEynAtsmR1+oY592oKysjIqKChYtWkRRURE9evRg0qRJdOrUiYsvrrk/cLt27dL1CwoK2Lx5MzFG+vTpQ2VlZa321q5dyz777ENVVdUOj5268W+t7R/84AeceOKJPPTQQyxfvpwTTjgBgFGjRjFo0CAeffRRhg8fzp133kmMkTFjxnDjjTfu5rsgSZIktR5Zr2EKIXwrhLAIODyEsDDj8b/AwuYLMXcMHjyY2bNn07lzZwoKCujcuTNr1qyhsrKS0tLSrK87/PDDee+999IJ06ZNm6iurqZTp0706tWLBx98EIAYI3/729/qbGPGH/8IwHPPPUdhYSGFhYV8+OGHHHTQQQBMnTo1Xfe1117j0EMP5bLLLuOss85i4cKFnHzyycyYMYN3330XgH/+85+8/vrru/2eSJIkqWU64Omq9COf1bfow++AL1KzwMMXMx79Y4wXNkNsOadv376sXr2a4447rta+wsJCunTpkvV1bdu2ZcaMGXz3u9/l6KOPpqSkJL2AxLRp07jrrrs4+uij6dOnDw8//HCdbezbqRMnXngh48eP56677gLg2muvZcKECQwePLjWAg7Tp0+nqKiIkpISli5dyte+9jWOOuoofvaznzFs2DCKi4s59dRT0wtPSJIkSbkq65S8GOOHwIfAVwBCCF2puXHt3iGEvWOMK5onxMbXkGXAm0JBQUGtpcSh9sjOCSeckJ4WB3DbbbelyyUlJcydO3e7Nnv16sUfU6NHmS699tJ0+fF77kmXOxQVpculpaX84x//SG//9Kc/BWDChAlMmDBhuzZHjhzJyJEj6zo1SZIkKSc1ZFnxL4YQlgH/C/wZWA78TxPHJUmSJEmJ22HCBPwMOA74R4yxF3Ay8HyTRiVJkiRJLUBDEqZNMcb3gT1CCHvEGJ8GSpo4LkmSJElKXEOWFV8TQtgbeBaYFkJ4l5ob2EqSJElSTmvICNPZwHrgCuCPwKvUrJYnSZIkSTlthyNMMcb/CyEcAvSOMd4bQtgLKGj60CRJkiQpWQ1ZJe8bwAzgP1O7DgJ+35RB5aK99967SdufOnUqb775Znp72DHD+OD9D5r0mJIkSVKua8g1TJcCA4G/AMQYl6XuydRqrbzu2UZtr/vEIY3a3q6YOnUqRUVFdOvWLelQJEmS6ldeWHu718HJxCE1QEMSpo0xxk9CCACEENoAsUmjyhPvvfce48ePZ8WKmnsAT548mcGDB1NeXs6KFSt47bXXWLFiBVdccQWXXXYZUHNz2WnTptGjRw+6dOlC//796dmzJ/Pnz2f06NF06NCByspKAKbdOY0/P/5n9tiwifsmTeLwQw9N7FwlSZKk1qghiz78OYTwPaBDCOFU4EHgD00bVn64/PLLufLKK3nxxReZOXMmY8eOTT+3dOlSHn/8cebNm8ePf/xjNm3axPz585k5cyYvvfQSs2bNYv78+QCcd955DBgwgGnTplFVVUWHDh0A2Lfzvjz41IOMHTmSyffem8g5SpKk1mfJEUemH1K+a8gI03XAvwGLgG8CjwF3NmVQ+eLJJ5/k5ZdfTm+vXbuWjz76CIAzzjiDdu3a0a5dO7p27co777zDc889x9lnn51OiL74xfoXKzzlzFMA6HfUUTzy5JNNdBaSJElS7sqaMIUQDo4xrogxbgV+k3qoEW3dupXKysp0ApSpXbt26XJBQQGbN28mxp2bCdm2bdt/vX7Llt0LVpIkScpD9U3JS6+EF0KY2Qyx5J1hw4Zx2223pberqqrqrX/88cfzhz/8gY8//ph169bx6KOPpp/r2LFjenRKkiRJUuOob0peyCi7WsBuWr9+Pd27d09vX3XVVfzyl7/k0ksvpbi4mM2bNzN06FCmTJmStY1jjz2Ws846i6OPPppDDjmEAQMGUFhYs8rMRRddxPjx42st+iBJkiRp99SXMMUs5VYviWXAt27dWuf+6dOnb7evvLy81vbixYvT5WuuuYby8nLWr1/P0KFDufrqqwE499xzOffcc9P1nvjrE+ly/z59ePyee3YnfEmSJCkv1ZcwHR1CWEvNSFOHVJnUdowxdmry6LSdcePG8fLLL/Pxxx8zZswYjjnmmKRDkiRJknJW1oQpxljQnIGoYX73u98lHYIkSZKUNxpyHyZJkiRJyksNuQ+TJLVIPa/710qRy9snGIgStfK6Z9Pl5r5GNcljS5KahwmTJDWD28c/lS5fOuWkBCORtK1tF1vadlstjx9WtHy59HfPhElKiKMj0q6bNPLMdHlkr+8mGIkkKdd5DVMzufLKK5k8eXJ6e/jw4YwdOza9ffXVV3PDDTdw3nnn1fn6E044gfnz5wNwww03pPcvX76coqKiJopakiRJym95OcLU2EPtDWmvrKyMBx98kCuuuIKtW7eyevVq1q5dm36+oqKCyZMn873vfW+Hbd1www0NqidJkiRp9zjC1EwGDx5MRUUFANXV1RQVFdGxY0c++OADNm7cyJIlS9h3333To0UbNmzgggsuoLi4mJEjR7JhwwYArrvuOjZs2EBJSQmjR48GYMuWLXzjG9+gT58+DBs2LF1XkiQpV0waeWb6ITUnE6Zm0q1bN9q0acOKFSuoqKigtLSUQYMGUVlZyfz58ykuLqZt27bp+r/+9a/Za6+9WLhwIddffz0LFiwAYOLEiXTo0IGqqiqmTZsGwLJly7j00kuprq5mn332YebMmYmcoyRJkpRrTJia0aejTJ8mTKWlpentsrKyWnXnzp3LhRdeCEBxcTHFxcVZ2+3VqxclJSUA9O/fn+XLlzfZOUiSJEn5JC+vYUpKWVkZFRUVLFq0iKKiInr06MGkSZPo1KkTF1988Xb1QwgNarddu3bpckFBgVPyJKkJuUKfJOUXR5ia0eDBg5k9ezadO3emoKCAzp07s2bNGiorKyktLa1Vd+jQoekpd4sXL2bhwoXp5/bcc082bdrUrLFLkiRJjWHldc+mH62BCVMz6tu3L6tXr+a4446rta+wsJAuXbrUqvutb32LdevWUVxczM0338zAgQPTz40bN47i4uL0og+SpIbred2j6YckSTuSl1PykrqDd0FBQa2lxAGmTp2aLvfs2ZPFixcD0KFDB+6///4627npppu46aab0tufvgbgmmuuAaB6dXVjhS1JkiTlrbxMmCTltr739k2XF41ZlGAkkiSptXNKniRJkiRl4QiT1IItOeLIdPnIpUsSjERqfeY8dVi6fPJJryYYiSSpNcubhCnG2OBlutX0YoxJhyApB2VeozpkaHJxSJJyR15MyWvfvj3vv/++/6S3EDFG3n//fdq3b590KJIkSVK98mKEqXv37qxcuZL33nsv6VCazdvr3k6Xt2QszLdnQUEC0Wyvffv2dO/ePekwJEk57vbxT6XLl045KcFItCsy+09KSl4kTHvuuSe9evVq9uMmuVLXl+/9crr8wI2b02Wvg5EkSdLOyrx33fKJZyQYSfPLi4RJkqSdkbngCvhhkyTls7y4hkmSJEmSdoUjTJKk/FVemFH+MLk4JEktlgmT1MJkXvv2QIJx5KvMZakzy8pvXnguSfkr0YQphHAa8AugALgzxjhxm+fbAf8F9AfeB0bGGJc3d5yS8pM3PpWaz7YfUPiBhaSWIrGEKYRQANwOnAqsBF4MITwSY3w5o9q/AR/EGP9fCOEC4CZgZPNHK0mSmpMfWEhqKZIcYRoIvBJjfA0ghHA/cDaQmTCdDZSnyjOA20IIIXoHWklSI3M6rCSpLkkmTAcBb2RsrwQGZasTY9wcQvgQ2A9Y3SwRSo3sgKer0uX2CcahRubCAZKkfJL5d6/XwcnF0UxCUoM1IYTzgeExxrGp7a8CA2OM386oU52qszK1/WqqzvvbtDUOGAdw8MEH93/99deb6Sy2uYlX+1G1n8z4xynznh6Z9/OYNPLMdHlkr++my3e2n5MuDxn623R5dJiZLrd/fFWDjp0p88Lljz+4dYfHzqs55Bk//H0zfviz3fg3s+8Arp4+uwmDy953YP/VJ9vPXqaV1z2bLnefOKTOOpnJLmzz85dxA79aoxQN+N7J177L+rszy+9N2L17IWX239snluxyO/XJ2wVDduMDg4b87ME2HzZl+du3s7+3M3/26jt2rqnv/5bM93DRmEU7bGtnf3dm+725u/L2Zy+LhvzPCQ37v7OxpsM29/9MDRVCWBBjHLCjekmOMK0EemRsdwfezFJnZQihDVAI/HPbhmKMdwB3AAwYMMDpepKkWpoqSZIk5b4kb1z7ItA7hNArhNAWuAB4ZJs6jwBjUuXzgKe8fkmSJElSc0lshCl1TdK/A49Ts6z43THG6hDCT4D5McZHgLuA34YQXqFmZOmCpOJVfsmcirDkxiPrqSlJkqRcluh9mGKMjwGPbbPvhxnlj4HzmzsuSZIkSYJkp+RJkiRJUouW6AiTJEnSLstclS9jhUpJakwmTJIkSVIey1yOfc5Tv81eMU85JU+SJEmSsnCESZIkSVKTaSk3qt1VJky7qdadqssTC0OSJEnabSef9GrSIbQ4TsmTJEmSpCwcYZIkSVKTqzUrR2pFHGGSJEmSpCwcYWomRy5dknQIkiRJknaSCZMkNcDbJ5bU2u75+KqEIpEkSc3JKXmSJEmSlIUjTJIkKRHdJw5JOgRJ2iFHmCRJkiQpCxMmSZIkScrCKXmStAu8n4gk7di2C+ZIrZEjTJIkSZKUhSNMkiRJarXKy8uTDkE5zhEmSZIkScrCESZJkhqBn3JLUm4yYZIkSZJyxJFLlyQdQs4xYZIkSXnh6umz0+WV1z2bYCSSWhOvYZIkSZKkLBxhSpifdkmSJEktlyNMkiRJkpSFCZMkSZIkZWHCJEmSJElZeA2TJElq0d4+sSRd7vn4qgQjkZSPHGGSJEmSpCxMmCRJkiQpCxMmSZIkScrCa5hakO4Th/xro3xOcoFIkiRJAhxhkiRJkqSsTJgkSZIkKQun5EmSJIlFYxYlHYLUIpkwNabyD5OOQJIkSVIjMmGSJEmSctzV02fX2l553bMJRdL6mDBJUgtRXl6edAiSJGkbJkyS1IgyrwFYcuORCUYiSZIagwmTtIu2HdqWJElS7jFhkiRJrcbyiWfUud/RXUlNxfswSZIkSVIWjjBJkqSccuTSJUmHICmHOMIkSZIkSVmYMEmSJElSFiZMkiRJkpSFCZMkSZIkZeGiD5KkZJV/mHQEkiRlZcIkSZLyTveJQ5IOQVIrYcIkSZKUjxzdlRrEa5gkSZIkKQtHmKRW4tIpJ6XLk0bemmAkkiRJ+SOREaYQQucQwp9CCMtSX/eto05JCKEyhFAdQlgYQhiZRKySJEmS8ldSU/KuA+bEGHsDc1Lb21oPfC3G2Ac4DZgcQtinGWOUJEmSlOeSSpjOBu5Nle8FvrRthRjjP2KMy1LlN4F3gf2bLUJJkiRJeS+phOmzMca3AFJfu9ZXOYQwEGgLvNoMsUmSJEkS0ISLPoQQngQOqOOp63eynQOB3wJjYoxbs9QZB4wDOPjgg3cyUkmSJEmqW5MlTDHGU7I9F0J4J4RwYIzxrVRC9G6Wep2AR4HvxxhfqOdYdwB3AAwYMCDuXuSSJEmSVCOpZcUfAcYAE1NfH962QgihLfAQ8F8xxgebNzzpX45cuiTpECRJkhpV94lDkg6h1UgqYZoIPBBC+DdgBXA+QAhhADA+xjgW+DIwFNgvhHBR6nUXxRirEohXkiTVpfzDpCOQpCaVSMIUY3wfOLmO/fOBsanyfcB9zRyaJEmSJKUlNcIkqYmUl5cnHYIkSVLOSGpZcUmSJElq8UyYJEmSJCkLp+RJn/LCZUmSJG3DhEmSJClPLJ94RtIhSK2OU/IkSZIkKQsTJkmSJEnKwoRJkiRJkrLwGiYB0H3ikH9tlM9JLhApAbW+/yVJkjI4wiRJkiRJWTjCJElN5MilS5IOQZIk7SZHmCRJkiQpC0eY8tjV02cnHYIkSZLUopkwtVDl5eWZW/8qPl3VzJFIkiRJ+cspeZIkSZKUhQmTJEmSJGXhlDwpB3gfIUmSpKZhwiRJanbLJ56RdAiSJDWIU/IkSZIkKQsTJkmSJEnKwil5knLakUuXJB2CJElqxUyYJKmZZd40euV1zyYYiSRJ2hETJm2n9k1zJUmSpPzlNUySJEmSlIUJkyRJkiRlYcIkSZIkSVl4DZMkqUVyhUNJUkvgCJMkSZIkZeEIk9QKZS5LLUmSpKZjwpQryj9MOgJJkiQp5zglT5IkSZKyMGGSJEmSpCxMmCRJkiQpCxMmSZIkScrCRR9aseUTz0g6BEmSJCmnmTDlmUunnJR0CJIkSVKr4ZQ8SZIkScrCESZJSlD3iUOSDkGSJNXDhKmVefvEkqRDkCRJkvKGU/IkSZIkKQsTJkmSJEnKwoRJkiRJkrIwYZIkSZKkLEyYJEmSJCkLEyZJkiRJysKESZIkSZKyMGGSJEmSpCxMmCRJkiQpCxMmSZIkScrChEmSJEmSsjBhkiRJkqQsTJgkSZIkKYtEEqYQQucQwp9CCMtSX/etp26nEMKqEMJtzRmjJEmSJCU1wnQdMCfG2BuYk9rO5qfAn5slKkmSJEnKkFTCdDZwb6p8L/CluiqFEPoDnwWeaKa4JEmSJCktqYTpszHGtwBSX7tuWyGEsAcwCfhOM8cmSZIkSQC0aaqGQwhPAgfU8dT1DWziEuCxGOMbIYQdHWscMA7g4IMP3pkwJUmSJCmrJkuYYoynZHsuhPBOCOHAGONbIYQDgXfrqFYKDAkhXALsDbQNIayLMW53vVOM8Q7gDoABAwbExjkDSZIkSfmuyRKmHXgEGANMTH19eNsKMcbRn5ZDCBcBA+pKliRJkiSpqSR1DdNE4NQQwjLg1NQ2IYQBIYQ7E4pJkiRJkmpJZIQpxvg+cHId++cDY+vYPxWYrIWJvAAABtpJREFU2uSBSZIkSVKGpKbkSZIkqRXrPnFI0iFIzSKpKXmSJEmS1OKZMEmSJElSFiZMkiRJkpSFCZMkSZIkZWHCJEmSJElZmDBJkiRJUhYmTJIkSZKUhQmTJEmSJGVhwiRJkiRJWZgwSZIkSVIWJkySJEmSlIUJkyRJkiRlYcIkSZIkSVmYMEmSJElSFiZMkiRJkpSFCZMkSZIkZWHCJEmSJElZmDBJkiRJUhYmTJIkSZKURYgxJh1DowohvAe8nnQcTagLsDrpILTL7L/Wy75r3ey/1s3+a73su9Yt1/vvkBjj/juqlHMJU64LIcyPMQ5IOg7tGvuv9bLvWjf7r3Wz/1ov+651s/9qOCVPkiRJkrIwYZIkSZKkLEyYWp87kg5Au8X+a73su9bN/mvd7L/Wy75r3ew/vIZJkiRJkrJyhEmSJEmSsjBh2kUhhC0hhKoQQnUI4W8hhKtCCHuknhsQQvhlQnFVNFI756fObWsIIadWR8mDvvt5CGFpCGFhCOGhEMI+jdFuS5EH/ffTVN9VhRCeCCF0a4x2W4pc77+M9q4JIcQQQpfGbDdJud53IYTyEMKq1DlWhRBOb4x2W4pc779UW98OIfw9dY43N1a7Scv1vgshTM/4uVseQqhqjHYbk1PydlEIYV2Mce9UuSvwO+D5GOOPko2scYQQjgS2Av8JXBNjnJ9wSI0mD/puGPBUjHFzCOEmgBjjdxMOq9HkQf91ijGuTZUvA46KMY5POKxGk+v9BxBC6AHcCRwB9I8x5sQ9THK970II5cC6GOMtScfSFPKg/04ErgfOiDFuDCF0jTG+m3RcjSHX+y5TCGES8GGM8SdJx1JLjNHHLjyo+aWauX0o8D4QgBOA2an95cC9wBPAcuAc4GZgEfBHYM9Uvf7An4EFwOPAgan9zwA3AfOAfwBDUvv7pPZVAQuB3plxpeL4ObA4dayRqf0npNqcASwFppFKnLOc5zPAgKTfb/tu5/su9ZoRwLSk33P7b5f7bwLw66Tfc/tv5/ovVefoVNxdkn7P7buG9V0q7muSfp/tv13uvweAU5J+n+273fqfMwBvfNp+S3okHkBrfWz7zZva9wHw2Tq+eZ8D9qTmD+h64Aup5x4CvpR6rgLYP7V/JHB3qvwMMClVPh14MlX+FTA6VW4LdMiMCzgX+BNQkIppBXBgKrYPge7UTMmsBI6v5zyfIccTplztu1RbfwAuTPo9t/92rv+A/6Dmj8biT2PLlUeu9x9wFvCLVHk5OZww5WDflaf6bCFwN7Bv0u+5/bdT/VcF/Bj4CzXJwLFJv+f23U7/zzkUmJ/0+13Xow1qTCHL/v+JMW4KISyi5pvpj6n9i4CewOFAEfCnEAKpOm9lvH5W6uuCVH2o+aa7PoTQHZgVY1y2zTGPB/47xrgFeCeE8GfgWGAtMC/GuBIgNU+0JzU/YPks5/ouhHA9sJmaT3RyXU71X4zx+tQxJgD/DvxoB+ff2uVE/4UQ9qJmStCwhp54DsiJvkv5NfBTIKa+TgIurv/0W71c6r82wL7AcanXPRBCODSm/hPPQbnUd5/6CvDf2U85OS760EhCCIcCW4C65stuBIgxbgU2ZfzwbqXmBzwA1THGktSjb4xx2LavT7XfJtXW76j5JHMD8HgI4aRtQ6on3I0Z5XSb+SoX+y6EMAY4k5pPhHL1jwWQm/2X4XfUfHKXs3Ks/w4DegF/CyEsp+ZT1b+GEA6op81WK8f6jhjjOzHGLamYfwMMrKe9Vi/X+g9YSc0/8zHGOC8Va84supIpB/uOEEIbaqYQTq+nrcSYMDWCEML+wBTgtl385/TvwP4hhNJUe3uGEPrs4JiHAq/FGH8JPAIUb1NlLjAyhFCQim8oNfNPlSEX+y6EcBrwXeCsGOP6hp9K65Oj/dc7Y/MsauZ956Rc678Y46IYY9cYY88YY09q/oE7Jsb49k6dVSuQa32Xav/AjM0R1EyJzUm52H/A74GTUsf6HDVTx3JiwZVMOdp3AKcASz8djWpp8npkYTd1SA0t7knNtKffArfuSkMxxk9CCOcBvwwhFFLTL5OB6npeNhK4MISwCXgb2HY1kYeAUuBv1EwvuDbG+HYI4YiGxBRCGEHNnNX9gUdDCFUxxuE7c14tWE73HXAb0I5/Dbe/EHNolTVyv/8mhhAOp+bTwNeBXOo7yP3+y2W53nc3hxBKUq9dDnyzoefTSuR6/90N3B1CWAx8AozJoRkWud53ABfQQqfjgcuKS5IkSVJWTsmTJEmSpCxMmCRJkiQpCxMmSZIkScrChEmSJEmSsjBhkiRJkqQsTJgkSZIkKQsTJkmSJEnKwoRJkiRJkrL4/9VTt9DYtl1LAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97533f2828>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97533825f8>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f97528ed390>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for i in range(1, 10):\n",
+    "    pca, X_pca = do_pca(i, df)\n",
+    "    pca_df = pca_results(df, pca)\n",
+    "    print(f\"{pca_df['Explained Variance'].sum()} {i}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Code to find number of components providing more than \n",
+    "# 85% of variance explained\n",
+    "\n",
+    "num_comps = 6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Nice job!  That's right!  With 6 components, you can explain more than 85% of the variability in the original dataset.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"https://bit.ly/2cKTiso\">"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Now check your answer here to complete this mini project!\n",
+    "display.HTML(t.question_check_six(num_comps))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_SC.ipynb b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_SC.ipynb
new file mode 100644
index 0000000..dd8ef2e
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/PCA_SC.ipynb	
@@ -0,0 +1,1049 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "PCA is commonly used with high dimensional data.  One type of high dimensional data is images. In this example, I will show you a similar use case using images of numbers.\n",
+    "\n",
+    "A classic example of working with image data is the MNIST dataset, which was open sourced in the late 1990s by researchers across Microsoft, Google, and NYU.  I have linked more information about the dataset below this video in the workbook:  http://yann.lecun.com/exdb/mnist/\n",
+    "\n",
+    "To get started, let's import the libraries we will need for the rest of the notebook."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from sklearn.decomposition import PCA\n",
+    "from sklearn.preprocessing import StandardScaler\n",
+    "from sklearn.ensemble import RandomForestClassifier\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import confusion_matrix, accuracy_score\n",
+    "\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The dataset has 42,000 images in the training dataset, and another 28,000 images in a test set.  Let's read in the datasets and see what they look like.  If you would like to follow along with me, you can open the workspace below this video in another window and work along with me.  Let's take a closer look at the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "train = pd.read_csv('./data/train.csv')\n",
+    "train.fillna(0, inplace=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Loading the data may take a bit of time, but once it is loaded, we will focus on the training dataset. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>label</th>\n",
+       "      <th>pixel0</th>\n",
+       "      <th>pixel1</th>\n",
+       "      <th>pixel2</th>\n",
+       "      <th>pixel3</th>\n",
+       "      <th>pixel4</th>\n",
+       "      <th>pixel5</th>\n",
+       "      <th>pixel6</th>\n",
+       "      <th>pixel7</th>\n",
+       "      <th>pixel8</th>\n",
+       "      <th>...</th>\n",
+       "      <th>pixel774</th>\n",
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+       "      <th>pixel778</th>\n",
+       "      <th>pixel779</th>\n",
+       "      <th>pixel780</th>\n",
+       "      <th>pixel781</th>\n",
+       "      <th>pixel782</th>\n",
+       "      <th>pixel783</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
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+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 785 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  \\\n",
+       "0      1       0       0       0       0       0       0       0       0   \n",
+       "1      0       0       0       0       0       0       0       0       0   \n",
+       "2      1       0       0       0       0       0       0       0       0   \n",
+       "3      4       0       0       0       0       0       0       0       0   \n",
+       "4      0       0       0       0       0       0       0       0       0   \n",
+       "\n",
+       "   pixel8    ...     pixel774  pixel775  pixel776  pixel777  pixel778  \\\n",
+       "0       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "1       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "2       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "3       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "4       0    ...          0.0       0.0       0.0       0.0       0.0   \n",
+       "\n",
+       "   pixel779  pixel780  pixel781  pixel782  pixel783  \n",
+       "0       0.0       0.0       0.0       0.0       0.0  \n",
+       "1       0.0       0.0       0.0       0.0       0.0  \n",
+       "2       0.0       0.0       0.0       0.0       0.0  \n",
+       "3       0.0       0.0       0.0       0.0       0.0  \n",
+       "4       0.0       0.0       0.0       0.0       0.0  \n",
+       "\n",
+       "[5 rows x 785 columns]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "train.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>label</th>\n",
+       "      <th>pixel0</th>\n",
+       "      <th>pixel1</th>\n",
+       "      <th>pixel2</th>\n",
+       "      <th>pixel3</th>\n",
+       "      <th>pixel4</th>\n",
+       "      <th>pixel5</th>\n",
+       "      <th>pixel6</th>\n",
+       "      <th>pixel7</th>\n",
+       "      <th>pixel8</th>\n",
+       "      <th>...</th>\n",
+       "      <th>pixel774</th>\n",
+       "      <th>pixel775</th>\n",
+       "      <th>pixel776</th>\n",
+       "      <th>pixel777</th>\n",
+       "      <th>pixel778</th>\n",
+       "      <th>pixel779</th>\n",
+       "      <th>pixel780</th>\n",
+       "      <th>pixel781</th>\n",
+       "      <th>pixel782</th>\n",
+       "      <th>pixel783</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>6304.000000</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>6304.000000</td>\n",
+       "      <td>6304.000000</td>\n",
+       "      <td>6304.000000</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "      <td>6304.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>4.440355</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.139594</td>\n",
+       "      <td>0.142291</td>\n",
+       "      <td>0.026967</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>2.885613</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>5.099940</td>\n",
+       "      <td>5.531089</td>\n",
+       "      <td>1.675547</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>2.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
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+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>4.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>7.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>9.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>...</td>\n",
+       "      <td>253.000000</td>\n",
+       "      <td>253.000000</td>\n",
+       "      <td>130.000000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>8 rows × 785 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  \\\n",
+       "count  6304.000000  6304.0  6304.0  6304.0  6304.0  6304.0  6304.0  6304.0   \n",
+       "mean      4.440355     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "std       2.885613     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "min       0.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "25%       2.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "50%       4.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "75%       7.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "max       9.000000     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
+       "\n",
+       "       pixel7  pixel8    ...        pixel774     pixel775     pixel776  \\\n",
+       "count  6304.0  6304.0    ...     6304.000000  6304.000000  6304.000000   \n",
+       "mean      0.0     0.0    ...        0.139594     0.142291     0.026967   \n",
+       "std       0.0     0.0    ...        5.099940     5.531089     1.675547   \n",
+       "min       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "25%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "50%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "75%       0.0     0.0    ...        0.000000     0.000000     0.000000   \n",
+       "max       0.0     0.0    ...      253.000000   253.000000   130.000000   \n",
+       "\n",
+       "       pixel777  pixel778  pixel779  pixel780  pixel781  pixel782  pixel783  \n",
+       "count    6304.0    6304.0    6304.0    6304.0    6304.0    6304.0    6304.0  \n",
+       "mean        0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "std         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "min         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "25%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "50%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "75%         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "max         0.0       0.0       0.0       0.0       0.0       0.0       0.0  \n",
+       "\n",
+       "[8 rows x 785 columns]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "train.describe()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From a header and the describe of the data, we can see that the data has a label column with what digit was created, and the pixels for each part of the image are the features.  The values for the pixels are between 0 and 255.  You can find an article on the pixel values in the article below in the notebook. https://homepages.inf.ed.ac.uk/rbf/HIPR2/value.htm\n",
+    "\n",
+    "Given what we know about the data, let's split the label off and put the images in their own matrix."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "train.fillna(0, inplace=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# save the labels to a Pandas series target\n",
+    "y = train['label']\n",
+    "# Drop the label feature\n",
+    "X = train.drop(\"label\",axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52cfffeb70>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.countplot(y, color = sns.color_palette()[0]); #a very quick look at the data shows that all the labels appear roughly 4k times"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's take a look at what a few of the numbers look like with this little helper function. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_images(num_images):\n",
+    "    '''\n",
+    "    This function plots the num_images provided of MNIST dataset. \n",
+    "    \n",
+    "    INPUT: num_images - int - The number of images you would like to view.\n",
+    "           Mod 10 of num_images should be 0 and it should be fewer than 101 images.\n",
+    "    OUTPUT: A figure with the images shown for the training data.\n",
+    "    '''\n",
+    "    if num_images % 10 == 0 and num_images <= 100:\n",
+    "        for digit_num in range(0,num_images): \n",
+    "            plt.subplot(num_images/10,10,digit_num+1) #create subplots\n",
+    "            mat_data = X.iloc[digit_num].as_matrix().reshape(28,28)  #reshape images\n",
+    "            plt.imshow(mat_data) #plot the data\n",
+    "            plt.xticks([]) #removes numbered labels on x-axis\n",
+    "            plt.yticks([]) #removes numbered labels on y-axis\n",
+    "    else:\n",
+    "        print('That is not the right input, please read the docstring before continuing.')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:12: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  if sys.path[0] == '':\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52cffc85f8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "show_images(100)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Some of these look pretty easy to identify, and others not so much... I wrote another helper function to be able to see each of the first 50 images of any one type of number."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_images_by_digit(digit_to_see):\n",
+    "    '''\n",
+    "    This function plots the digits_to_see provided of MNIST dataset. \n",
+    "    \n",
+    "    INPUT: digits_to_see - int - A number between 0 and 9 of what you want to see.\n",
+    "    OUTPUT: A figure with the images shown for the training data.\n",
+    "    '''\n",
+    "    if digit_to_see in list(range(10)):\n",
+    "        indices = np.where(y == digit_to_see) # pull indices for num of interest\n",
+    "        for digit_num in range(0,50): \n",
+    "            plt.subplot(5,10, digit_num+1) #create subplots\n",
+    "            mat_data = X.iloc[indices[0][digit_num]].as_matrix().reshape(28,28)  #reshape images\n",
+    "            plt.imshow(mat_data) #plot the data\n",
+    "            plt.xticks([]) #removes numbered labels on x-axis\n",
+    "            plt.yticks([]) #removes numbered labels on y-axis   \n",
+    "    else:\n",
+    "        print('That is not the right input, please read the docstring before continuing.')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:12: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  if sys.path[0] == '':\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52c83a75c0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "show_images_by_digit(1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Some of these ones are pretty wild looking...  One common way to use PCA is to reduce the dimensionality of high dimensionality data that you want to use for prediction, but the results seem to be overfitting (potentially because their is a lot of noise in the data.  Which can certainly be the case with image data).\n",
+    "\n",
+    "Let's take a first pass on creating a simple model to predict the values of the images using all of the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[205   0   0   0   0   0   4   0   0   0]\n",
+      " [  0 234   3   0   1   0   1   2   2   0]\n",
+      " [  1   4 211   1   3   0   1   7   0   0]\n",
+      " [  2   0   5 171   0   6   0   1   4   2]\n",
+      " [  0   0   1   0 165   1   4   0   0   7]\n",
+      " [  2   1   0   4   1 174   2   1   1   0]\n",
+      " [  3   0   1   0   0   2 204   1   0   0]\n",
+      " [  0   0   6   1   5   0   0 205   2   6]\n",
+      " [  1   1   2   7   0   3   0   1 185   2]\n",
+      " [  2   1   0   2  13   2   0   2   3 183]]\n",
+      "AxesSubplot(0.125,0.125;0.62x0.755)\n",
+      "0.930802498799\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0.93080249879865451"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52c9000208>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Because we will fit this more than once, might as well make a function\n",
+    "def fit_random_forest_classifier(X, y):\n",
+    "    '''\n",
+    "    INPUT: names are pretty self explanatory\n",
+    "    OUTPUT: none - prints the confusion matrix and accuracy\n",
+    "    '''\n",
+    "    #First let's create training and testing data\n",
+    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
+    "\n",
+    "    #We could grid search and tune, but let's just fit a simple model to see how it does\n",
+    "    #instantiate\n",
+    "    clf = RandomForestClassifier(n_estimators=100, max_depth=None)\n",
+    "\n",
+    "    #fit\n",
+    "    clf.fit(X_train, y_train)\n",
+    "\n",
+    "    #predict\n",
+    "    y_preds = clf.predict(X_test)\n",
+    "\n",
+    "    #score\n",
+    "    mat = confusion_matrix(y_test, y_preds)\n",
+    "    print(mat)\n",
+    "    print(sns.heatmap(mat, annot=True, cmap='bwr', linewidths=.5))\n",
+    "    acc = accuracy_score(y_test, y_preds)\n",
+    "    print(acc)\n",
+    "    return acc\n",
+    "    \n",
+    "fit_random_forest_classifier(X, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The above model does pretty well on the test set using all of the data, let's see how we well a model can do with a much lower number of features.  Perhaps, we can do as well or better by reducing the noise in the original features.\n",
+    "\n",
+    "Working with unsupervised techniques in scikit learn follows a similar process as working with supervised techniques, but excludes predicting and scoring, and instead we just need to transform our data.  Often the fit and transform are done all in one step.\n",
+    "\n",
+    "1. Instantiate\n",
+    "2. Fit \n",
+    "3. Transform \n",
+    "\n",
+    "It is worth mentioning that because all of our features are on the same scale from 0 to 255, scaling isn't super necessary here.  At the same time, I usually try to create processes that are extendible without having to think and dive into the details again.  Without standardizing, this process would only work for data that was already scaled.\n",
+    "\n",
+    "You can use the below function to perform PCA on this dataset, but also any other dataset."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def do_pca(n_components, data):\n",
+    "    '''\n",
+    "    Transforms data using PCA to create n_components, and provides back the results of the\n",
+    "    transformation.\n",
+    "    \n",
+    "    INPUT: n_components - int - the number of principal components to create\n",
+    "           data - the data you would like to transform\n",
+    "           \n",
+    "    OUTPUT: pca - the pca object created after fitting the data\n",
+    "            X_pca - the transformed X matrix with new number of components\n",
+    "    '''\n",
+    "    X = StandardScaler().fit_transform(data)\n",
+    "    pca = PCA(n_components)\n",
+    "    X_pca = pca.fit_transform(X)\n",
+    "    return pca, X_pca"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pca, X_pca = do_pca(2, X)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(6304, 2)"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X_pca.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[108   0  46   8   6  10  26   0   5   0]\n",
+      " [  0 207   0   4   2   7   4   5   8   6]\n",
+      " [ 40   2  67  28  15  22  33   1  16   4]\n",
+      " [  9   1  27  22  27  29  25  10  25  16]\n",
+      " [  5   4  17  17  50  16  16  12  12  29]\n",
+      " [  9   8  31  23  16  20  30   4  34  11]\n",
+      " [ 33   6  53  17   8  28  32   4  28   2]\n",
+      " [  3   5   1   8  38  10   3  95   8  54]\n",
+      " [  7   7  24  29  22  30  30   9  34  10]\n",
+      " [  2  12   4  17  30  10   4  53  10  66]]\n",
+      "AxesSubplot(0.125,0.125;0.62x0.755)\n",
+      "0.336857280154\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0.3368572801537722"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52c86c8eb8>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fit_random_forest_classifier(X_pca, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So, let's look at the positives first... that was super fast.  But clearly two components isn't giving us enough information to clearly identify the digits.  Let's consider a few more components, and take a closer look at what we know about the components."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(2, 784)"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pca.components_.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_components(X, y):\n",
+    "    '''\n",
+    "    plots the data in a 2 dimensional space to view separation\n",
+    "    INPUT: pretty straightforward again\n",
+    "    OUTPUT: none\n",
+    "    '''\n",
+    "    x_min, x_max = np.min(X, 0), np.max(X, 0)\n",
+    "    X = (X - x_min) / (x_max - x_min)\n",
+    "    plt.figure(figsize=(10, 6))\n",
+    "    for i in range(X.shape[0]):\n",
+    "        plt.text(X[i, 0], X[i, 1], str(y[i]), color=plt.cm.Set1(y[i]), fontdict={'size': 15})\n",
+    "\n",
+    "    plt.xticks([]), plt.yticks([]), plt.ylim([-0.1,1.1]), plt.xlim([-0.1,1.1])\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f52cfff0550>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_components(X_pca[:100], y[:100])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/cars.csv b/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/cars.csv
new file mode 100644
index 0000000..4ec64a1
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/cars.csv	
@@ -0,0 +1,388 @@
+Sports,SUV,Wagon,Minivan,Pickup,AWD,RWD,Retail,Dealer,Engine,Cylinders,Horsepower,CityMPG,HighwayMPG,Weight,Wheelbase,Length,Width
+Acura 3.5 RL,0,0,0,0,0,0,0,43755,39014,3.5,6,225,18,24,3880,115,197,72
+Acura 3.5 RL Navigation,0,0,0,0,0,0,0,46100,41100,3.5,6,225,18,24,3893,115,197,72
+Acura MDX,0,1,0,0,0,1,0,36945,33337,3.5,6,265,17,23,4451,106,189,77
+Acura NSX S,1,0,0,0,0,0,1,89765,79978,3.2,6,290,17,24,3153,100,174,71
+Acura RSX,0,0,0,0,0,0,0,23820,21761,2.0,4,200,24,31,2778,101,172,68
+Acura TL,0,0,0,0,0,0,0,33195,30299,3.2,6,270,20,28,3575,108,186,72
+Acura TSX,0,0,0,0,0,0,0,26990,24647,2.4,4,200,22,29,3230,105,183,69
+Audi A4 1.8T,0,0,0,0,0,0,0,25940,23508,1.8,4,170,22,31,3252,104,179,70
+Audi A4 1.8T convertible,0,0,0,0,0,0,0,35940,32506,1.8,4,170,23,30,3638,105,180,70
+Audi A4 3.0 convertible,0,0,0,0,0,0,0,42490,38325,3.0,6,220,20,27,3814,105,180,70
+Audi A4 3.0,0,0,0,0,0,0,0,31840,28846,3.0,6,220,20,28,3462,104,179,70
+Audi A4 3.0 Quattro manual,0,0,0,0,0,1,0,33430,30366,3.0,6,220,17,26,3583,104,179,70
+Audi A4 3.0 Quattro auto,0,0,0,0,0,1,0,34480,31388,3.0,6,220,18,25,3627,104,179,70
+Audi A4 3.0 Quattro convertible,0,0,0,0,0,1,0,44240,40075,3.0,6,220,18,25,4013,105,180,70
+Audi A6 2.7 Turbo Quattro four-door,0,0,0,0,0,1,0,42840,38840,2.7,6,250,18,25,3836,109,192,71
+Audi A6 3.0,0,0,0,0,0,0,0,36640,33129,3.0,6,220,20,27,3561,109,192,71
+Audi A6 3.0 Avant Quattro,0,0,1,0,0,1,0,40840,37060,3.0,6,220,18,25,4035,109,192,71
+Audi A6 3.0 Quattro,0,0,0,0,0,1,0,39640,35992,3.0,6,220,18,25,3880,109,192,71
+Audi A6 4.2 Quattro,0,0,0,0,0,1,0,49690,44936,4.2,8,300,17,24,4024,109,193,71
+Audi A8 L Quattro,0,0,0,0,0,1,0,69190,64740,4.2,8,330,17,24,4399,121,204,75
+Audi S4 Avant Quattro,0,0,1,0,0,1,0,49090,44446,4.2,8,340,15,21,3936,104,179,70
+Audi S4 Quattro,0,0,0,0,0,1,0,48040,43556,4.2,8,340,14,20,3825,104,179,70
+Audi RS 6,1,0,0,0,0,0,0,84600,76417,4.2,8,450,15,22,4024,109,191,78
+Audi TT 1.8,1,0,0,0,0,0,0,35940,32512,1.8,4,180,20,28,3131,95,159,73
+Audi TT 1.8 Quattro,1,0,0,0,0,1,0,37390,33891,1.8,4,225,20,28,2921,96,159,73
+Audi TT 3.2,1,0,0,0,0,1,0,40590,36739,3.2,6,250,21,29,3351,96,159,73
+BMW 325i,0,0,0,0,0,0,1,28495,26155,2.5,6,184,20,29,3219,107,176,69
+BMW 325Ci,0,0,0,0,0,0,1,30795,28245,2.5,6,184,20,29,3197,107,177,69
+BMW 325Ci convertible,0,0,0,0,0,0,1,37995,34800,2.5,6,184,19,27,3560,107,177,69
+BMW 325xi,0,0,0,0,0,1,0,30245,27745,2.5,6,184,19,27,3461,107,176,69
+BMW 325xi Sport,0,0,1,0,0,1,0,32845,30110,2.5,6,184,19,26,3594,107,176,69
+BMW 330Ci,0,0,0,0,0,0,1,36995,33890,3.0,6,225,20,30,3285,107,176,69
+BMW 330Ci convertible,0,0,0,0,0,0,1,44295,40530,3.0,6,225,19,28,3616,107,177,69
+BMW 330i,0,0,0,0,0,0,1,35495,32525,3.0,6,225,20,30,3285,107,176,69
+BMW 330xi,0,0,0,0,0,1,0,37245,34115,3.0,6,225,20,29,3483,107,176,69
+BMW 525i four-door,0,0,0,0,0,0,1,39995,36620,2.5,6,184,19,28,3428,114,191,73
+BMW 530i four-door,0,0,0,0,0,0,1,44995,41170,3.0,6,225,20,30,3472,114,191,73
+BMW 545iA four-door,0,0,0,0,0,0,1,54995,50270,4.4,8,325,18,26,3814,114,191,73
+BMW 745i four-door,0,0,0,0,0,0,1,69195,63190,4.4,8,325,18,26,4376,118,198,75
+BMW 745Li four-door,0,0,0,0,0,0,1,73195,66830,4.4,8,325,18,26,4464,123,204,75
+BMW M3,1,0,0,0,0,0,1,48195,44170,3.2,6,333,16,24,3415,108,177,70
+BMW M3 convertible,1,0,0,0,0,0,1,56595,51815,3.2,6,333,16,23,3781,108,177,70
+BMW X3 3.0i,0,1,0,0,0,1,0,37000,33873,3.0,6,225,16,23,4023,110,180,73
+BMW X5 4.4i,0,1,0,0,0,1,0,52195,47720,4.4,8,325,16,22,4824,111,184,74
+BMW Z4 convertible 2.5i two-door,1,0,0,0,0,0,1,33895,31065,2.5,6,184,20,28,2932,98,161,70
+BMW Z4 convertible 3.0i two-door,1,0,0,0,0,0,1,41045,37575,3.0,6,225,21,29,2998,98,161,70
+Buick Century Custom,0,0,0,0,0,0,0,22180,20351,3.1,6,175,20,30,3353,109,195,73
+Buick LeSabre Custom four-door,0,0,0,0,0,0,0,26470,24282,3.8,6,205,20,29,3567,112,200,74
+Buick LeSabre Limited,0,0,0,0,0,0,0,32245,29566,3.8,6,205,20,29,3591,112,200,74
+Buick Park Avenue,0,0,0,0,0,0,0,35545,32244,3.8,6,205,20,29,3778,114,207,75
+Buick Park Avenue Ultra,0,0,0,0,0,0,0,40720,36927,3.8,6,240,18,28,3909,114,207,75
+Buick Rainier,0,1,0,0,0,1,0,37895,34357,4.2,6,275,15,21,4600,113,193,75
+Buick Regal GS,0,0,0,0,0,0,0,28345,26047,3.8,6,240,18,28,3536,109,196,73
+Buick Regal LS,0,0,0,0,0,0,0,24895,22835,3.8,6,200,20,30,3461,109,196,73
+Buick Rendezvous CX,0,1,0,0,0,0,0,26545,24085,3.4,6,185,19,26,4024,112,187,74
+Cadillac CTS VVT,0,0,0,0,0,0,1,30835,28575,3.6,6,255,18,25,3694,113,190,71
+Cadillac Deville,0,0,0,0,0,0,0,45445,41650,4.6,8,275,18,26,3984,115,207,74
+Cadillac Deville DTS,0,0,0,0,0,0,0,50595,46362,4.6,8,300,18,26,4044,115,207,74
+Cadillac Escaladet,0,1,0,0,0,0,0,52795,48377,5.3,8,295,14,18,5367,116,199,79
+Cadillac Seville,0,0,0,0,0,0,0,47955,43841,4.6,8,275,18,26,3992,112,201,75
+Cadillac SRX V8,0,1,0,0,0,0,0,46995,43523,4.6,8,320,16,21,4302,116,195,73
+Cadillac XLR,1,0,0,0,0,0,1,76200,70546,4.6,8,320,17,25,3647,106,178,72
+Chevrolet Aveo,0,0,0,0,0,0,0,11690,10965,1.6,4,103,28,34,2370,98,167,66
+Chevrolet Astro,0,0,0,1,0,1,0,26395,23954,4.3,6,190,14,17,4605,111,190,78
+Chevrolet Aveo LS,0,0,0,0,0,0,0,12585,11802,1.6,4,103,28,34,2348,98,153,66
+Chevrolet Cavalier two-door,0,0,0,0,0,0,0,14610,13697,2.2,4,140,26,37,2617,104,183,69
+Chevrolet Cavalier four-door,0,0,0,0,0,0,0,14810,13884,2.2,4,140,26,37,2676,104,183,68
+Chevrolet Cavalier LS,0,0,0,0,0,0,0,16385,15357,2.2,4,140,26,37,2617,104,183,69
+Chevrolet Corvette,1,0,0,0,0,0,1,44535,39068,5.7,8,350,18,25,3246,105,180,74
+Chevrolet Corvette convertible,1,0,0,0,0,0,1,51535,45193,5.7,8,350,18,25,3248,105,180,74
+Chevrolet Impala,0,0,0,0,0,0,0,21900,20095,3.4,6,180,21,32,3465,111,200,73
+Chevrolet Impala LS,0,0,0,0,0,0,0,25000,22931,3.8,6,200,20,30,3476,111,200,73
+Chevrolet Impala SS,0,0,0,0,0,0,0,27995,25672,3.8,6,240,18,28,3606,111,200,73
+Chevrolet Malibu,0,0,0,0,0,0,0,18995,17434,2.2,4,145,24,34,3174,106,188,70
+Chevrolet Malibu LS,0,0,0,0,0,0,0,20370,18639,3.5,6,200,22,30,3297,106,188,70
+Chevrolet Malibu LT,0,0,0,0,0,0,0,23495,21551,3.5,6,200,23,32,3315,106,188,70
+Chevrolet Malibu Maxx,0,0,1,0,0,0,0,22225,20394,3.5,6,200,22,30,3458,112,188,70
+Chevrolet Monte Carlo LS,0,0,0,0,0,0,0,21825,20026,3.4,6,180,21,32,3340,111,198,73
+Chevrolet Monte Carlo SS,0,0,0,0,0,0,0,24225,22222,3.8,6,200,18,28,3434,111,198,73
+Chevrolet Suburban 1500 LT,0,1,0,0,0,0,0,42735,37422,5.3,8,295,14,18,4947,130,219,79
+Chevrolet Tahoe LT,0,1,0,0,0,1,0,41465,36287,5.3,8,295,14,18,5050,116,197,79
+Chevrolet Tracker,0,1,0,0,0,0,0,20255,19108,2.5,6,165,19,22,2866,98,163,67
+Chevrolet TrailBlazer LT,0,1,0,0,0,0,0,30295,27479,4.2,6,275,16,21,4425,113,192,75
+Chevrolet Venture LS,0,0,0,1,0,0,0,27020,24518,3.4,6,185,19,26,3699,112,187,72
+Chrysler 300M,0,0,0,0,0,0,0,29865,27797,3.5,6,250,18,27,3581,113,198,74
+Chrysler 300M Special Edition,0,0,0,0,0,0,0,33295,30884,3.5,6,255,18,27,3650,113,198,74
+Chrysler Concorde LX,0,0,0,0,0,0,0,24130,22452,2.7,6,200,21,29,3479,113,208,74
+Chrysler Concorde LXi,0,0,0,0,0,0,0,26860,24909,3.5,6,232,19,27,3548,113,208,74
+Chrysler Crossfire,1,0,0,0,0,0,1,34495,32033,3.2,6,215,17,25,3060,95,160,70
+Chrysler Pacifica,0,0,1,0,0,0,1,31230,28725,3.5,6,250,17,23,4675,116,199,79
+Chrysler PT Cruiser,0,0,0,0,0,0,0,17985,16919,2.4,4,150,22,29,3101,103,169,67
+Chrysler PT Cruiser GT,0,0,0,0,0,0,0,25955,24172,2.4,4,220,21,27,3217,103,169,67
+Chrysler PT Cruiser Limited,0,0,0,0,0,0,0,22000,20573,2.4,4,150,22,29,3105,103,169,67
+Chrysler Sebring,0,0,0,0,0,0,0,19090,17805,2.4,4,150,22,30,3173,108,191,71
+Chrysler Sebring Touring,0,0,0,0,0,0,0,21840,20284,2.7,6,200,21,28,3222,108,191,71
+Chrysler Sebring convertible,0,0,0,0,0,0,0,25215,23451,2.4,4,150,22,30,3357,106,194,64
+Chrysler Sebring Limited convertible,0,0,0,0,0,0,0,30950,28613,2.7,6,200,21,28,3448,106,194,69
+Chrysler Town and Country LX,0,0,0,1,0,0,0,27490,25371,3.3,6,180,19,26,4068,119,201,79
+Chrysler Town and Country Limited,0,0,0,1,0,0,0,38380,35063,3.8,6,215,18,25,4331,119,201,79
+Dodge Caravan SE,0,0,0,1,0,0,0,21795,20508,2.4,4,150,20,26,3862,113,189,79
+Dodge Durango SLT,0,1,0,0,0,1,0,32235,29472,4.7,8,230,15,21,4987,119,201,76
+Dodge Grand Caravan SXT,0,0,0,1,0,1,0,32660,29812,3.8,6,215,18,25,4440,119,201,79
+Dodge Intrepid ES,0,0,0,0,0,0,0,24885,23058,3.5,6,232,18,27,3487,113,204,75
+Dodge Intrepid SE,0,0,0,0,0,0,0,22035,20502,2.7,6,200,21,29,3469,113,204,75
+Dodge Neon SE,0,0,0,0,0,0,0,13670,12849,2.0,4,132,29,36,2581,105,174,67
+Dodge Neon SXT,0,0,0,0,0,0,0,15040,14086,2.0,4,132,29,36,2626,105,174,67
+Dodge Stratus SXT,0,0,0,0,0,0,0,18820,17512,2.4,4,150,21,28,3182,108,191,71
+Dodge Stratus SE,0,0,0,0,0,0,0,20220,18821,2.4,4,150,21,28,3175,108,191,71
+Ford Crown Victoria,0,0,0,0,0,0,1,24345,22856,4.6,8,224,17,25,4057,115,212,78
+Ford Crown Victoria LX,0,0,0,0,0,0,1,27370,25105,4.6,8,224,17,25,4057,115,212,78
+Ford Crown Victoria LX Sport,0,0,0,0,0,0,1,30315,27756,4.6,8,239,17,25,4057,115,212,78
+Ford Escape XLS,0,1,0,0,0,1,0,22515,20907,3.0,6,201,18,23,3346,103,173,70
+Ford Expedition 4.6 XLT,0,1,0,0,0,0,0,34560,30468,4.6,8,232,15,19,5000,119,206,79
+Ford Explorer XLT V6,0,1,0,0,0,1,0,29670,26983,4.0,6,210,15,20,4463,114,190,72
+Ford Focus LX,0,0,0,0,0,0,0,13730,12906,2.0,4,110,27,36,2606,103,168,67
+Ford Focus SE,0,0,0,0,0,0,0,15460,14496,2.0,4,130,26,33,2606,103,168,67
+Ford Focus SVT,0,0,0,0,0,0,0,19135,17878,2.0,4,170,21,28,2750,103,168,67
+Ford Focus ZTW,0,0,1,0,0,0,0,17475,16375,2.0,4,130,26,33,2702,103,178,67
+Ford Focus ZX5,0,0,0,0,0,0,0,15580,14607,2.0,4,130,26,33,2691,103,168,67
+Ford Focus ZX3,0,0,0,0,0,0,0,13270,12482,2.0,4,130,26,33,2612,103,168,67
+Ford Freestar SE,0,0,0,1,0,0,0,26930,24498,3.9,6,193,17,23,4275,121,201,77
+Ford Mustang,1,0,0,0,0,0,1,18345,16943,3.8,6,193,20,29,3290,101,183,73
+Ford Mustang GT Premium,1,0,0,0,0,0,1,29380,26875,4.6,8,260,17,25,3347,101,183,73
+Ford Taurus LX,0,0,0,0,0,0,0,20320,18881,3.0,6,155,20,27,3306,109,198,73
+Ford Taurus SE,0,0,1,0,0,0,0,22290,20457,3.0,6,155,19,26,3497,109,198,73
+Ford Taurus SES Duratec,0,0,0,0,0,0,0,22735,20857,3.0,6,201,19,26,3313,109,198,73
+Ford Thunderbird Deluxe,1,0,0,0,0,0,0,37530,34483,3.9,8,280,17,24,3780,107,186,72
+GMC Envoy XUV SLE,0,1,0,0,0,0,0,31890,28922,4.2,6,275,15,19,4945,129,208,75
+GMC Safari SLE,0,0,0,1,0,0,1,25640,23215,4.3,6,190,16,20,4309,111,190,78
+GMC Yukon 1500 SLE,0,1,0,0,0,0,0,35725,31361,4.8,8,285,16,19,5042,116,199,79
+GMC Yukon XL 2500 SLT,0,1,0,0,0,1,0,46265,40534,6.0,8,325,13,17,6133,130,219,79
+Honda Accord EX,0,0,0,0,0,0,0,22260,20080,2.4,4,160,26,34,3047,105,188,71
+Honda Accord EX V6,0,0,0,0,0,0,0,26960,24304,3.0,6,240,21,30,3294,105,188,71
+Honda Accord LX,0,0,0,0,0,0,0,19860,17924,2.4,4,160,26,34,2994,105,188,71
+Honda Accord LX V6,0,0,0,0,0,0,0,23760,21428,3.0,6,240,21,30,3349,108,190,72
+Honda Civic EX,0,0,0,0,0,0,0,17750,16265,1.7,4,127,32,37,2601,103,175,68
+Honda Civic DX,0,0,0,0,0,0,0,13270,12175,1.7,4,115,32,38,2432,103,175,67
+Honda Civic HX,0,0,0,0,0,0,0,14170,12996,1.7,4,117,36,44,2500,103,175,67
+Honda Civic LX,0,0,0,0,0,0,0,15850,14531,1.7,4,115,32,38,2513,103,175,68
+Honda Civic Si,0,0,0,0,0,0,0,19490,17849,2.0,4,160,26,30,2782,101,166,67
+Honda Civic Hybrid,0,0,0,0,0,0,0,20140,18451,1.4,4,93,46,51,2732,103,175,68
+Honda CR-V LX,0,1,0,0,0,1,0,19860,18419,2.4,4,160,21,25,3258,103,179,70
+Honda Element LX,0,1,0,0,0,1,0,18690,17334,2.4,4,160,21,24,3468,101,167,72
+Honda Insight,0,0,0,0,0,0,0,19110,17911,2.0,3,73,60,66,1850,95,155,67
+Honda Odyssey EX,0,0,0,1,0,0,0,27450,24744,3.5,6,240,18,25,4365,118,201,76
+Honda Odyssey LX,0,0,0,1,0,0,0,24950,22498,3.5,6,240,18,25,4310,118,201,76
+Honda Pilot LX,0,1,0,0,0,1,0,27560,24843,3.5,6,240,17,22,4387,106,188,77
+Honda S2000,1,0,0,0,0,0,1,33260,29965,2.2,4,240,20,25,2835,95,162,69
+Hummer H2,0,1,0,0,0,1,0,49995,45815,6.0,8,316,10,12,6400,123,190,81
+Hyundai Accent,0,0,0,0,0,0,0,10539,10107,1.6,4,103,29,33,2255,96,167,66
+Hyundai Accent GL,0,0,0,0,0,0,0,11839,11116,1.6,4,103,29,33,2290,96,167,66
+Hyundai Accent GT,0,0,0,0,0,0,0,11939,11209,1.6,4,103,29,33,2339,96,167,66
+Hyundai Elantra GLS,0,0,0,0,0,0,0,13839,12781,2.0,4,138,26,34,2635,103,178,68
+Hyundai Elantra GT,0,0,0,0,0,0,0,15389,14207,2.0,4,138,26,34,2635,103,178,68
+Hyundai Elantra GT hatch,0,0,0,0,0,0,0,15389,14207,2.0,4,138,26,34,2698,103,178,68
+Hyundai Santa Fe GLS,0,1,0,0,0,0,0,21589,20201,2.7,6,173,20,26,3549,103,177,73
+Hyundai Sonata GLS,0,0,0,0,0,0,0,19339,17574,2.7,6,170,19,27,3217,106,187,72
+Hyundai Sonata LX,0,0,0,0,0,0,0,20339,18380,2.7,6,170,19,27,3217,106,187,72
+Hyundai Tiburon GT V6,1,0,0,0,0,0,0,18739,17101,2.7,6,172,19,26,3023,100,173,69
+Hyundai XG350,0,0,0,0,0,0,0,24589,22055,3.5,6,194,17,26,3651,108,192,72
+Hyundai XG350 L,0,0,0,0,0,0,0,26189,23486,3.5,6,194,17,26,3651,108,192,72
+Infiniti FX35,0,0,1,0,0,0,1,34895,31756,3.5,6,280,16,22,4056,112,189,76
+Infiniti FX45,0,0,1,0,0,1,0,36395,33121,4.5,8,315,15,19,4309,112,189,76
+Infiniti G35,0,0,0,0,0,0,1,28495,26157,3.5,6,260,18,26,3336,112,187,69
+Infiniti G35 Sport Coupe,0,0,0,0,0,0,1,29795,27536,3.5,6,280,18,26,3416,112,182,72
+Infiniti G35 AWD,0,0,0,0,0,1,0,32445,29783,3.5,6,260,18,26,3677,112,187,69
+Infiniti I35,0,0,0,0,0,0,0,31145,28320,3.5,6,255,19,26,3306,108,194,70
+Infiniti M45,0,0,0,0,0,0,1,42845,38792,4.5,8,340,17,23,3851,110,197,70
+Infiniti Q45 Luxury,0,0,0,0,0,0,1,52545,47575,4.5,8,340,17,23,3977,113,200,73
+Isuzu Ascender S,0,1,0,0,0,1,0,31849,29977,4.2,6,275,15,20,4967,129,208,76
+Isuzu Rodeo S,0,1,0,0,0,0,0,20449,19261,3.2,6,193,17,21,3836,106,178,70
+Jaguar S-Type 3.0,0,0,0,0,0,0,1,43895,40004,3.0,6,235,18,26,3777,115,192,72
+Jaguar S-Type 4.2,0,0,0,0,0,0,1,49995,45556,4.2,8,294,18,28,3874,115,192,72
+Jaguar S-Type R,0,0,0,0,0,0,1,63120,57499,4.2,8,390,17,24,4046,115,192,72
+Jaguar Vanden Plas,0,0,0,0,0,0,1,68995,62846,4.2,8,294,18,28,3803,119,200,73
+Jaguar X-Type 2.5,0,0,0,0,0,1,0,29995,27355,2.5,6,192,18,26,3428,107,184,70
+Jaguar X-Type 3.0,0,0,0,0,0,1,0,33995,30995,3.0,6,227,18,25,3516,107,184,70
+Jaguar XJ8,0,0,0,0,0,0,1,59995,54656,4.2,8,294,18,28,3803,119,200,73
+Jaguar XJR,0,0,0,0,0,0,1,74995,68306,4.2,8,390,17,24,3948,119,200,73
+Jaguar XK8 coupe,1,0,0,0,0,0,1,69995,63756,4.2,8,294,18,26,3779,102,187,71
+Jaguar XK8 convertible,1,0,0,0,0,0,1,74995,68306,4.2,8,294,18,26,3980,102,187,71
+Jaguar XKR coupe,1,0,0,0,0,0,1,81995,74676,4.2,8,390,16,23,3865,102,187,71
+Jaguar XKR convertible,1,0,0,0,0,0,1,86995,79226,4.2,8,390,16,23,4042,102,187,71
+Jeep Grand Cherokee Laredo,0,1,0,0,0,0,0,27905,25686,4.0,6,195,16,21,3790,106,181,72
+Jeep Liberty Sport,0,1,0,0,0,1,0,20130,18973,2.4,4,150,20,24,3826,104,174,72
+Jeep Wrangler Sahara,0,1,0,0,0,1,0,25520,23275,4.0,6,190,16,19,3575,93,150,67
+Kia Optima LX,0,0,0,0,0,0,0,16040,14910,2.4,4,138,23,30,3281,106,186,72
+Kia Optima LX V6,0,0,0,0,0,0,0,18435,16850,2.7,6,170,20,27,3279,106,186,72
+Kia Rio auto,0,0,0,0,0,0,0,11155,10705,1.6,4,104,25,32,2458,95,167,66
+Kia Rio manual,0,0,0,0,0,0,0,10280,9875,1.6,4,104,26,33,2403,95,167,66
+Kia Rio Cinco,0,0,1,0,0,0,0,11905,11410,1.6,4,104,26,33,2447,95,167,66
+Kia Sedona LX,0,0,0,1,0,0,0,20615,19400,3.5,6,195,16,22,4802,115,194,75
+Kia Sorento LX,0,1,0,0,0,0,0,19635,18630,3.5,6,192,16,19,4112,107,180,73
+Kia Spectra,0,0,0,0,0,0,0,12360,11630,1.8,4,124,24,32,2661,101,178,68
+Kia Spectra GS,0,0,0,0,0,0,0,13580,12830,1.8,4,124,24,32,2686,101,178,68
+Kia Spectra GSX,0,0,0,0,0,0,0,14630,13790,1.8,4,124,24,32,2697,101,178,68
+Land Rover Discovery SE,0,1,0,0,0,1,0,39250,35777,4.6,8,217,12,16,4576,100,185,74
+Land Rover Freelander SE,0,1,0,0,0,1,0,25995,23969,2.5,6,174,18,21,3577,101,175,71
+Land Rover Range Rover HSE,0,1,0,0,0,1,0,72250,65807,4.4,8,282,12,16,5379,113,195,76
+Lexus ES 330,0,0,0,0,0,0,0,32350,28755,3.3,6,225,20,29,3460,107,191,71
+Lexus GS 300,0,0,0,0,0,0,1,41010,36196,3.0,6,220,18,25,3649,110,189,71
+Lexus GS 430,0,0,0,0,0,0,1,48450,42232,4.3,8,300,18,23,3715,110,189,71
+Lexus GX 470,0,1,0,0,0,1,0,45700,39838,4.7,8,235,15,19,4740,110,188,74
+Lexus IS 300 manual,0,0,0,0,0,0,1,31045,27404,3.0,6,215,18,25,3255,105,177,68
+Lexus IS 300 auto,0,0,0,0,0,0,1,32415,28611,3.0,6,215,18,24,3285,105,177,68
+Lexus IS 300 SportCross,0,0,1,0,0,0,1,32455,28647,3.0,6,215,18,24,3410,105,177,68
+Lexus LS 430,0,0,0,0,0,0,1,55750,48583,4.3,8,290,18,25,3990,115,197,72
+Lexus LX 470,0,1,0,0,0,1,0,64800,56455,4.7,8,235,13,17,5590,112,193,76
+Lexus SC 430,1,0,0,0,0,0,1,63200,55063,4.3,8,300,18,23,3840,103,178,72
+Lexus RX 330,0,1,0,0,0,1,0,39195,34576,3.3,6,230,18,24,4065,107,186,73
+Lincoln Aviator Ultimate,0,1,0,0,0,0,0,42915,39443,4.6,8,302,13,18,4834,114,193,76
+Lincoln LS V6 Luxury,0,0,0,0,0,0,1,32495,29969,3.0,6,232,20,26,3681,115,194,73
+Lincoln LS V6 Premium,0,0,0,0,0,0,1,36895,33929,3.0,6,232,20,26,3681,115,194,73
+Lincoln LS V8 Sport,0,0,0,0,0,0,1,40095,36809,3.9,8,280,17,24,3768,115,194,73
+Lincoln LS V8 Ultimate,0,0,0,0,0,0,1,43495,39869,3.9,8,280,17,24,3768,115,194,73
+Lincoln Navigator Luxury,0,1,0,0,0,1,0,52775,46360,5.4,8,300,13,18,5969,119,206,80
+Lincoln Town Car Signature,0,0,0,0,0,0,1,41815,38418,4.6,8,239,17,25,4369,118,215,78
+Lincoln Town Car Ultimate,0,0,0,0,0,0,1,44925,41217,4.6,8,239,17,25,4369,118,215,78
+Lincoln Town Car Ultimate L,0,0,0,0,0,0,1,50470,46208,4.6,8,239,17,25,4474,124,221,78
+Mazda6 i,0,0,0,0,0,0,0,19270,17817,2.3,4,160,24,32,3042,105,187,70
+Mazda MPV ES,0,0,0,1,0,0,0,28750,26600,3.0,6,200,18,25,3812,112,188,72
+Mazda MX-5 Miata,1,0,0,0,0,0,1,22388,20701,1.8,4,142,23,28,2387,89,156,66
+Mazda MX-5 Miata LS,1,0,0,0,0,0,1,25193,23285,1.8,4,142,23,28,2387,89,156,66
+Mazda Tribute DX 2.0,0,1,0,0,0,1,0,21087,19742,2.0,4,130,22,25,3091,103,173,72
+Mercedes-Benz C32 AMG,0,0,0,0,0,0,1,52120,48522,3.2,6,349,16,21,3540,107,178,68
+Mercedes-Benz C230 Sport,0,0,0,0,0,0,1,26060,24249,1.8,4,189,22,30,3250,107,178,68
+Mercedes-Benz C240,0,0,1,0,0,0,1,33780,31466,2.6,6,168,19,25,3470,107,179,68
+Mercedes-Benz C240 RWD,0,0,0,0,0,0,1,32280,30071,2.6,6,168,20,25,3360,107,178,68
+Mercedes-Benz C240 AWD,0,0,0,0,0,1,0,33480,31187,2.6,6,168,19,25,3360,107,178,68
+Mercedes-Benz C320,0,0,0,0,0,0,1,37630,35046,3.2,6,215,20,26,3450,107,178,68
+Mercedes-Benz C320 Sport two-door,0,0,0,0,0,0,1,28370,26435,3.2,6,215,19,26,3430,107,178,68
+Mercedes-Benz C320 Sport four-door,0,0,0,0,0,0,1,35920,33456,3.2,6,215,19,26,3430,107,178,68
+Mercedes-Benz CL500,0,0,0,0,0,0,1,94820,88324,5.0,8,302,16,24,4085,114,196,73
+Mercedes-Benz CL600,0,0,0,0,0,0,1,128420,119600,5.5,12,493,13,19,4473,114,196,73
+Mercedes-Benz CLK320,0,0,0,0,0,0,1,45707,41966,3.2,6,215,20,26,3770,107,183,69
+Mercedes-Benz CLK500,0,0,0,0,0,0,1,52800,49104,5.0,8,302,17,22,3585,107,183,69
+Mercedes-Benz E320,0,0,1,0,0,0,1,50670,47174,3.2,6,221,19,27,3966,112,190,71
+Mercedes-Benz E320 four-door,0,0,0,0,0,0,1,48170,44849,3.2,6,221,19,27,3635,112,190,71
+Mercedes-Benz E500,0,0,1,0,0,1,0,60670,56474,5.0,8,302,16,24,4230,112,190,71
+Mercedes-Benz E500 four-door,0,0,0,0,0,0,1,57270,53382,5.0,8,302,16,20,3815,112,190,71
+Mercedes-Benz G500,0,1,0,0,0,1,0,76870,71540,5.0,8,292,13,14,5423,112,186,71
+Mercedes-Benz ML500,0,1,0,0,0,1,0,46470,43268,5.0,8,288,14,17,4874,111,183,72
+Mercedes-Benz S430,0,0,0,0,0,0,1,74320,69168,4.3,8,275,18,26,4160,122,203,73
+Mercedes-Benz S500,0,0,0,0,0,1,0,86970,80939,5.0,8,302,16,24,4390,122,203,73
+Mercedes-Benz SL500,1,0,0,0,0,0,1,90520,84325,5.0,8,302,16,23,4065,101,179,72
+Mercedes-Benz SL55 AMG,1,0,0,0,0,0,1,121770,113388,5.5,8,493,14,21,4235,101,179,72
+Mercedes-Benz SL600,1,0,0,0,0,0,1,126670,117854,5.5,12,493,13,19,4429,101,179,72
+Mercedes-Benz SLK230,1,0,0,0,0,0,1,40320,37548,2.3,4,192,21,29,3055,95,158,68
+Mercedes-Benz SLK32 AMG,1,0,0,0,0,0,1,56170,52289,3.2,6,349,17,22,3220,95,158,68
+Mercury Grand Marquis GS,0,0,0,0,0,0,1,24695,23217,4.6,8,224,17,25,4052,115,212,78
+Mercury Grand Marquis LS Premium,0,0,0,0,0,0,1,29595,27148,4.6,8,224,17,25,4052,115,212,78
+Mercury Grand Marquis LS Ultimate,0,0,0,0,0,0,1,30895,28318,4.6,8,224,17,25,4052,115,212,78
+Mercury Marauder,0,0,0,0,0,0,1,34495,31558,4.6,8,302,17,23,4195,115,212,78
+Mercury Monterey Luxury,0,0,0,1,0,0,0,33995,30846,4.2,6,201,16,23,4340,121,202,77
+Mercury Mountaineer,0,1,0,0,0,0,0,29995,27317,4.0,6,210,16,21,4374,114,190,72
+Mercury Sable GS,0,0,1,0,0,0,0,22595,20748,3.0,6,155,19,26,3488,109,198,73
+Mercury Sable GS four-door,0,0,0,0,0,0,0,21595,19848,3.0,6,155,20,27,3308,109,200,73
+Mercury Sable LS Premium,0,0,0,0,0,0,0,23895,21918,3.0,6,201,19,26,3315,109,200,73
+Mini Cooper,0,0,0,0,0,0,0,16999,15437,1.6,4,115,28,37,2524,97,143,67
+Mini Cooper S,0,0,0,0,0,0,0,19999,18137,1.6,4,163,25,34,2678,97,144,67
+Mitsubishi Diamante LS,0,0,0,0,0,0,0,29282,27250,3.5,6,205,18,25,3549,107,194,70
+Mitsubishi Eclipse GTS,1,0,0,0,0,0,0,25092,23456,3.0,6,210,21,28,3241,101,177,69
+Mitsubishi Eclipse Spyder GT,1,0,0,0,0,0,0,26992,25218,3.0,6,210,21,28,3296,101,177,69
+Mitsubishi Endeavor,0,1,0,0,0,1,0,30492,28330,3.8,6,215,17,21,4134,109,190,74
+Mitsubishi Galant,0,0,0,0,0,0,0,25700,23883,3.8,6,230,18,26,3649,108,191,72
+Mitsubishi Lancer Evolution,1,0,0,0,0,0,0,29562,27466,2.0,4,271,18,26,3263,103,179,70
+Mitsubishi Montero,0,1,0,0,0,1,0,33112,30763,3.8,6,215,15,19,4718,110,190,75
+Mitsubishi Outlander,0,1,0,0,0,0,0,18892,17569,2.4,4,160,21,27,3240,103,179,69
+Nissan 350Z,1,0,0,0,0,0,1,26910,25203,3.5,6,287,20,26,3188,104,169,72
+Nissan 350Z Enthusiast,1,0,0,0,0,0,1,34390,31845,3.5,6,287,20,26,3428,104,169,72
+Nissan Altima S,0,0,0,0,0,0,0,19240,18030,2.5,4,175,21,26,3039,110,192,70
+Nissan Altima SE,0,0,0,0,0,0,0,23290,21580,3.5,6,245,21,26,3197,110,192,70
+Nissan Maxima SE,0,0,0,0,0,0,0,27490,25182,3.5,6,265,20,28,3473,111,194,72
+Nissan Maxima SL,0,0,0,0,0,0,0,29440,26966,3.5,6,265,20,28,3476,111,194,72
+Nissan Murano,0,0,1,0,0,0,1,28739,27300,3.5,6,245,20,25,3801,111,188,74
+Nissan Pathfinder SE,0,1,0,0,0,0,0,27339,25972,3.5,6,240,16,21,3871,106,183,72
+Nissan Pathfinder Armada SE,0,1,0,0,0,0,0,33840,30815,5.6,8,305,13,19,5013,123,207,79
+Nissan Quest S,0,0,0,1,0,0,0,24780,22958,3.5,6,240,19,26,4012,124,204,78
+Nissan Quest SE,0,0,0,1,0,0,0,32780,30019,3.5,6,240,18,25,4175,124,204,78
+Nissan Sentra 1.8,0,0,0,0,0,0,0,12740,12205,1.8,4,126,28,35,2513,100,178,67
+Nissan Sentra 1.8 S,0,0,0,0,0,0,0,14740,13747,1.8,4,126,28,35,2581,100,178,67
+Nissan Sentra SE-R,0,0,0,0,0,0,0,17640,16444,2.5,4,165,23,28,2761,100,178,67
+Nissan Xterra XE,0,1,0,0,0,0,0,20939,19512,3.3,6,180,17,20,3760,104,178,70
+Oldsmobile Alero GLS,0,0,0,0,0,0,0,23675,21485,3.4,6,170,20,29,3085,107,187,70
+Oldsmobile Alero GX,0,0,0,0,0,0,0,18825,17642,2.2,4,140,24,32,2946,107,187,70
+Oldsmobile Silhouette GL,0,0,0,1,0,0,0,28790,26120,3.4,6,185,19,26,3948,120,201,72
+Pontiac Aztekt,0,1,0,0,0,0,0,21595,19810,3.4,6,185,19,26,3779,108,182,74
+Porsche Cayenne S,0,1,0,0,0,1,0,56665,49865,4.5,8,340,14,18,4950,112,188,76
+Pontiac Grand Am GT,0,0,0,0,0,0,0,22450,20595,3.4,6,175,20,29,3118,107,186,70
+Pontiac Grand Prix GT1,0,0,0,0,0,0,0,22395,20545,3.8,6,200,20,30,3477,111,198,74
+Pontiac Grand Prix GT2,0,0,0,0,0,0,0,24295,22284,3.8,6,200,20,30,3484,111,198,74
+Pontiac Montana,0,0,0,1,0,0,0,23845,21644,3.4,6,185,19,26,3803,112,187,72
+Pontiac Montana EWB,0,0,0,1,0,1,0,31370,28454,3.4,6,185,18,24,4431,121,201,72
+Pontiac Sunfire 1SA,0,0,0,0,0,0,0,15495,14375,2.2,4,140,24,33,2771,104,182,68
+Pontiac Sunfire 1SC,0,0,0,0,0,0,0,17735,16369,2.2,4,140,24,33,2771,104,182,68
+Pontiac Vibe,0,0,1,0,0,0,1,17045,15973,1.8,4,130,29,36,2701,102,172,70
+Porsche 911 Carrera,1,0,0,0,0,0,1,79165,69229,3.6,6,315,18,26,3135,93,175,70
+Porsche 911 Carrera 4S,1,0,0,0,0,1,0,84165,72206,3.6,6,315,17,24,3240,93,175,72
+Porsche 911 Targa,1,0,0,0,0,0,1,76765,67128,3.6,6,315,18,26,3119,93,175,70
+Porsche 911 GT2,1,0,0,0,0,0,1,192465,173560,3.6,6,477,17,24,3131,93,175,72
+Porsche Boxster,1,0,0,0,0,0,1,43365,37886,2.7,6,228,20,29,2811,95,170,70
+Porsche Boxster S,1,0,0,0,0,0,1,52365,45766,3.2,6,258,18,26,2911,95,170,70
+Saab 9-3 Arc,0,0,0,0,0,0,0,40670,38520,2.0,4,210,21,29,3480,105,182,69
+Saab 9-3 Arc Sport,0,0,0,0,0,0,0,30860,29269,2.0,4,210,20,28,3175,105,183,69
+Saab 9-3 Aero,0,0,0,0,0,0,0,33360,31562,2.0,4,210,20,28,3175,105,183,69
+Saab 9-3 Aero convertible,0,0,0,0,0,0,0,43175,40883,2.0,4,210,21,30,3700,105,182,69
+Saab 9-5 Arc,0,0,0,0,0,0,0,35105,33011,2.3,4,220,21,29,3470,106,190,71
+Saab 9-5 Aero,0,0,1,0,0,0,0,40845,38376,2.3,4,250,19,29,3620,106,190,71
+Saab 9-5 Aero four-door,0,0,0,0,0,0,0,39465,37721,2.3,4,250,21,29,3470,106,190,71
+Saturn Ion1,0,0,0,0,0,0,0,10995,10319,2.2,4,140,26,35,2692,103,185,67
+Saturn Ion2,           0,0,0,0,0,0,0,14300,13393,2.2,4,140,26,35,2692,103,185,67
+Saturn Ion2 quad coupe,0,0,0,0,0,0,0,14850,13904,2.2,4,140,26,35,2751,103,185,68
+Saturn Ion3,           0,0,0,0,0,0,0,15825,14811,2.2,4,140,26,35,2692,103,185,67
+Saturn Ion3 quad coupe,0,0,0,0,0,0,0,16350,15299,2.2,4,140,26,35,2751,103,185,68
+Saturn L300,           0,0,0,1,0,0,0,23560,21779,2.2,4,140,24,34,3109,107,190,69
+Saturn L300-2,0,0,0,0,0,0,0,21410,19801,3.0,6,182,20,28,3197,107,190,69
+Saturn VUE,0,1,0,0,0,1,0,20585,19238,2.2,4,143,21,26,3381,107,181,72
+Scion xA,0,0,0,0,0,0,0,12965,12340,1.5,4,108,32,38,2340,93,154,67
+Scion xB,0,0,1,0,0,0,0,14165,13480,1.5,4,108,31,35,2425,98,155,67
+Subaru Forester,0,0,1,0,0,1,0,21445,19646,2.5,4,165,21,28,3090,99,175,68
+Subaru Impreza 2.5 RS,0,0,0,0,0,1,0,19945,18399,2.5,4,165,22,28,2965,99,174,69
+Subaru Impreza WRX,1,0,0,0,0,1,0,25045,23022,2.0,4,227,20,27,3085,99,174,69
+Subaru Impreza WRX STi,1,0,0,0,0,1,0,31545,29130,2.5,4,300,18,24,3263,100,174,69
+Subaru Legacy GT,0,0,0,0,0,1,0,25645,23336,2.5,4,165,21,28,3395,104,184,69
+Subaru Legacy L,0,0,0,0,0,1,0,20445,18713,2.5,4,165,21,28,3285,104,184,69
+Subaru Outback,0,0,1,0,0,1,0,23895,21773,2.5,4,165,21,28,3430,104,187,69
+Subaru Outback Limited Sedan,0,0,0,0,0,1,0,27145,24687,2.5,4,165,20,27,3495,104,184,69
+Subaru Outback H6,0,0,0,0,0,1,0,29345,26660,3.0,6,212,19,26,3610,104,184,69
+Subaru Outback H-6 VDC,0,0,0,0,0,1,0,31545,28603,3.0,6,212,19,26,3630,104,184,69
+Suzuki Aeno S,0,0,0,0,0,0,0,12884,12719,2.3,4,155,25,31,2676,98,171,68
+Suzuki Aerio LX,0,0,0,0,0,0,0,14500,14317,2.3,4,155,25,31,2676,98,171,68
+Suzuki Aerio SX,0,0,1,0,0,1,0,16497,16291,2.3,4,155,24,29,2932,98,167,68
+Suzuki Forenza S,0,0,0,0,0,0,0,12269,12116,2.0,4,119,24,31,2701,102,177,68
+Suzuki Forenza EX,0,0,0,0,0,0,0,15568,15378,2.0,4,119,22,30,2756,102,177,68
+Suzuki Verona LX,0,0,0,0,0,0,0,17262,17053,2.5,6,155,20,27,3380,106,188,72
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diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/train.csv b/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/train.csv
new file mode 100644
index 0000000..412ebc4
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/data/train.csv	
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diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/helper_functions.py b/python/Unsupervised Learning/Dimensionality Reduction and PCA/helper_functions.py
new file mode 100644
index 0000000..f07406a
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/helper_functions.py	
@@ -0,0 +1,236 @@
+###########################################
+# Suppress matplotlib user warnings
+# Necessary for newer version of matplotlib
+import warnings
+warnings.filterwarnings("ignore", category = UserWarning, module = "matplotlib")
+#
+# Display inline matplotlib plots with IPython
+from IPython import get_ipython
+get_ipython().run_line_magic('matplotlib', 'inline')
+###########################################
+
+import pandas as pd
+import numpy as np
+from sklearn.decomposition import PCA
+from sklearn.preprocessing import StandardScaler
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.model_selection import train_test_split
+from sklearn.metrics import confusion_matrix, accuracy_score
+
+import matplotlib.image as mpimg
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+import seaborn as sns
+
+train = pd.read_csv('./data/train.csv')
+
+# save the labels to a Pandas series target
+y = train['label']
+
+# Drop the label feature
+X = train.drop("label",axis=1)
+
+def show_images(num_images):
+    '''
+    This function plots the num_images provided of MNIST dataset.
+
+    INPUT: int - The number of images you would like to view.
+           Mod 10 of num_images should be 0 and it should be fewer than 101 images.
+    OUTPUT: A figure with the images shown for the training data.
+    '''
+    if num_images % 10 == 0 and num_images <= 100:
+        for digit_num in range(0,num_images):
+            plt.subplot(num_images/10,10,digit_num+1) #create subplots
+            mat_data = X.iloc[digit_num].as_matrix().reshape(28,28)  #reshape images
+            plt.imshow(mat_data) #plot the data
+            plt.xticks([]) #removes numbered labels on x-axis
+            plt.yticks([]) #removes numbered labels on y-axis
+    else:
+        print('That is not the right input, please read the docstring before continuing.')
+
+
+def show_images_by_digit(digit_to_see):
+    '''
+    This function plots 50 images all of the type digits_to_see of the MNIST dataset.
+
+    INPUT: digits_to_see - int - A number between 0 and 9 of what you want to see.
+    OUTPUT: A figure with the images shown for the training data.
+    '''
+    if digit_to_see in list(range(10)):
+        indices = np.where(y == digit_to_see) # pull indices for num of interest
+        for digit_num in range(0,50):
+            plt.subplot(5,10, digit_num+1) #create subplots
+            mat_data = X.iloc[indices[0][digit_num]].as_matrix().reshape(28,28)  #reshape images
+            plt.imshow(mat_data) #plot the data
+            plt.xticks([]) #removes numbered labels on x-axis
+            plt.yticks([]) #removes numbered labels on y-axis
+    else:
+        print('That is not the right input, please read the docstring before continuing.')
+
+
+def fit_random_forest_classifier(X, y):
+    '''
+    INPUT: names are pretty self explanatory
+    OUTPUT: none - prints the confusion matrix and accuracy
+    '''
+    #First let's create training and testing data
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
+
+    #We could grid search and tune, but let's just fit a simple model to see how it does
+    #instantiate
+    clf = RandomForestClassifier(n_estimators=100, max_depth=None)
+
+    #fit
+    clf.fit(X_train, y_train)
+
+    #predict
+    y_preds = clf.predict(X_test)
+
+    #score
+    print(confusion_matrix(y_test, y_preds))
+    acc = accuracy_score(y_test, y_preds)
+    print(acc)
+    return acc
+
+
+def fit_random_forest_classifier2(X, y):
+    '''
+    INPUT: X - the x-matrix of input features
+           y - the response column
+    OUTPUT: none - prints the confusion matrix and accuracy
+    '''
+    #First let's create training and testing data
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
+
+    #We could grid search and tune, but let's just fit a simple model to see how it does
+    #instantiate
+    clf = RandomForestClassifier(n_estimators=100, max_depth=None)
+
+    #fit
+    clf.fit(X_train, y_train)
+
+    #predict
+    y_preds = clf.predict(X_test)
+
+    #score
+    acc = accuracy_score(y_test, y_preds)
+    return acc
+
+
+def do_pca(n_components, data):
+    '''
+    Transforms data using PCA to create n_components, and provides back the results of the
+    transformation.
+
+    INPUT: n_components - int - the number of principal components to create
+           data - the data you would like to transform
+
+    OUTPUT: pca - the pca object created after fitting the data
+            X_pca - the transformed X matrix with new number of components
+    '''
+    X = StandardScaler().fit_transform(data)
+    pca = PCA(n_components)
+    X_pca = pca.fit_transform(X)
+    return pca, X_pca
+
+
+def plot_components(X, y):
+    '''
+    plots the data in a 2 dimensional space to view separation
+    INPUT: X - the x-matrix of input features
+           y - the response column
+    OUTPUT: none
+    '''
+    x_min, x_max = np.min(X, 0), np.max(X, 0)
+    X = (X - x_min) / (x_max - x_min)
+    plt.figure(figsize=(10, 6))
+    for i in range(X.shape[0]):
+        plt.text(X[i, 0], X[i, 1], str(y[i]), color=plt.cm.Set1(y[i]), fontdict={'size': 15})
+
+    plt.xticks([]), plt.yticks([]), plt.ylim([-0.1,1.1]), plt.xlim([-0.1,1.1])
+
+
+def scree_plot(pca):
+    '''
+    Creates a scree plot associated with the principal components
+
+    INPUT: pca - the result of instantian of PCA in scikit learn
+
+    OUTPUT:
+            None
+    '''
+    num_components=len(pca.explained_variance_ratio_)
+    ind = np.arange(num_components)
+    vals = pca.explained_variance_ratio_
+
+    plt.figure(figsize=(10, 6))
+    ax = plt.subplot(111)
+    cumvals = np.cumsum(vals)
+    ax.bar(ind, vals)
+    ax.plot(ind, cumvals)
+    for i in range(num_components):
+        ax.annotate(r"%s%%" % ((str(vals[i]*100)[:4])), (ind[i]+0.2, vals[i]), va="bottom", ha="center", fontsize=12)
+
+    ax.xaxis.set_tick_params(width=0)
+    ax.yaxis.set_tick_params(width=2, length=12)
+
+    ax.set_xlabel("Principal Component")
+    ax.set_ylabel("Variance Explained (%)")
+    plt.title('Explained Variance Per Principal Component')
+
+
+def plot_component(pca, comp):
+    '''
+    Plots an image associated with each component to understand how the weighting
+    of the components
+    INPUT:
+          pca - pca object created from PCA in sklearn
+          comp - int - the component you want to see starting at 0
+    OUTPUT
+          None
+    '''
+    if comp <= len(pca.components_):
+        mat_data = np.asmatrix(pca.components_[comp]).reshape(28,28)  #reshape images
+        plt.imshow(mat_data); #plot the data
+        plt.xticks([]) #removes numbered labels on x-axis
+        plt.yticks([]) #removes numbered labels on y-axis
+    else:
+        print('That is not the right input, please read the docstring before continuing.')
+
+
+def pca_results(full_dataset, pca):
+    '''
+    Create a DataFrame of the PCA results
+    Includes dimension feature weights and explained variance
+    Visualizes the PCA results
+    '''
+
+    # Dimension indexing
+    dimensions = dimensions = ['Dimension {}'.format(i) for i in range(1,len(pca.components_)+1)]
+
+    # PCA components
+    components = pd.DataFrame(np.round(pca.components_, 4), columns = full_dataset.keys())
+    components.index = dimensions
+
+    # PCA explained variance
+    ratios = pca.explained_variance_ratio_.reshape(len(pca.components_), 1)
+    variance_ratios = pd.DataFrame(np.round(ratios, 4), columns = ['Explained Variance'])
+    variance_ratios.index = dimensions
+
+    # Create a bar plot visualization
+    fig, ax = plt.subplots(figsize = (14,8))
+
+    # Plot the feature weights as a function of the components
+    components.plot(ax = ax, kind = 'bar');
+    ax.set_ylabel("Feature Weights")
+    ax.set_xticklabels(dimensions, rotation=0)
+
+
+    # Display the explained variance ratios
+    for i, ev in enumerate(pca.explained_variance_ratio_):
+        ax.text(i-0.40, ax.get_ylim()[1] + 0.05, "Explained Variance\n          %.4f"%(ev))
+
+    # Return a concatenated DataFrame
+    return pd.concat([variance_ratios, components], axis = 1)
+
+
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code.py b/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code.py
new file mode 100644
index 0000000..4419c5f
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code.py	
@@ -0,0 +1,68 @@
+import pandas as pd
+import numpy as np
+from sklearn.decomposition import PCA
+from sklearn.preprocessing import StandardScaler
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.model_selection import train_test_split
+from sklearn.metrics import confusion_matrix, accuracy_score
+from helper_functions import show_images, show_images_by_digit
+from helper_functions import fit_random_forest_classifier, do_pca, plot_components
+
+import matplotlib.image as mpimg
+import matplotlib.pyplot as plt
+import seaborn as sns
+
+train = pd.read_csv('./data/train.csv')
+
+# save the labels to a Pandas series target
+y = train['label']
+
+# Drop the label feature
+X = train.drop("label", axis=1)
+
+def question_two_check(input1, input2):
+    match1 = (input1 == y)
+    match2 = (input2 == X)
+    if all(match1) and all(match2):
+        print("That looks right!")
+    else:
+        print("Oops!  That doesn't look like what was expected for X and y.  X should be a matrix of only the pixels, and y should only hold the label column.")
+
+
+def question_3_check(solution_three):
+    a = True
+    b = False
+    c = 6.13
+    d = 'The total amount of variability in the data explained by the first two principal components'
+    e = None
+    my_sol = {
+    '10.42' : d,
+    'The first component will ALWAYS have the most amount of variability explained.': a,
+    'The total amount of variability in the data explained by the first component': c,
+    'The sum of the variability explained by all the components can be greater than 100%': b
+}
+
+    if my_sol == solution_three:
+        print("Looks good!  The amount of variability explained by each principal component gives us an idea of how much of the original variability in the original data is retained by each component.  Nice job matching these up!")
+
+    if my_sol['10.42'] != solution_three['10.42']:
+        print("Oops!  Looks like you missed the first one.  Notice that 9.85 is the sum of the two bars shown in the plot.  This means that the total amount of variability explained by the first two principal components is 9.85.  5.74% can be explained by the first component, and the rest is explained by the second component.\n\n")
+    if my_sol['The first component will ALWAYS have the most amount of variability explained.'] != solution_three['The first component will ALWAYS have the most amount of variability explained.']:
+        print("Oops!  Looks like you missed the second one.  It is actually the case that the first component will ALWAYS be the largest.  This is because PCA tries to find the direction of maximum variance first. In fact, the components will always be in order from largest amount of variability explained first to smallest amount of variability explained as the last component.\n\n")
+    if my_sol['The total amount of variability in the data explained by the first component'] != solution_three['The total amount of variability in the data explained by the first component']:
+        print("Oops!  Looks like you missed the third one.  The amount of variability explained by each component is shown by the bars in the chart.  The total amount of variability explained by the combined components up to each component is shown by the line.  This gives us an idea of how much is explained so far, and how much each additional component is contributing.\n\n")
+    if my_sol['The sum of the variability explained by all the components can be greater than 100%'] != solution_three['The sum of the variability explained by all the components can be greater than 100%']:
+        print("Oops!  The last answer doesn't look right.  Your principal components are always reducing the original space of your features until you have as many principal components as you had original features.  Therefore, the sum of the amount of variability explained by all the components can never exceep 100%")
+
+
+def question_5_check(solution_five):
+
+    my_sol = {
+    'This component looks like it will assist in identifying zero': 0,
+    'This component looks like it will assist in identifying three': 3
+    }
+
+    if my_sol == solution_five:
+        print("Nice job!  That matches our solution as well!  The index of the first principal component appears to have really high weights where a zero would appear.  Alternatively, the fourth (third indexed component) appears to downweight where a three would appear to make it stand out.")
+    else:
+        print("Oops!  That doesn't look quite right.  Please use the indices as numbers for the values, so the first component should be 0, the second component would be 1, and so on.")
diff --git a/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code2.py b/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code2.py
new file mode 100644
index 0000000..4787a74
--- /dev/null
+++ b/python/Unsupervised Learning/Dimensionality Reduction and PCA/test_code2.py	
@@ -0,0 +1,114 @@
+import pandas as pd
+import numpy as np
+from sklearn.decomposition import PCA
+from sklearn.preprocessing import StandardScaler
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.model_selection import train_test_split
+from sklearn.metrics import confusion_matrix, accuracy_score
+from helper_functions import show_images, show_images_by_digit
+from helper_functions import fit_random_forest_classifier, do_pca, plot_components
+
+import matplotlib.image as mpimg
+import matplotlib.pyplot as plt
+import seaborn as sns
+
+def display_gif(fn):
+    return '<img src="{}">'.format(fn)
+
+
+def check_question_one(solution_1_dict):
+    a = 7
+    b = 66
+    c = 387
+    d = 18
+    e = 0.23
+    f = 0.05
+
+    my_sol = {
+        'The number of cars in the dataset': c,
+        'The number of car features in the dataset': d,
+        'The number of dummy variables in the dataset': a,
+        'The proportion of minivans in the dataset': f,
+        'The max highway mpg for any car': b
+    }
+
+    if my_sol == solution_1_dict:
+        print("Nice job!  Looks like your dataset matches what we found!")
+        return display_gif('https://bit.ly/2K9X0gD')
+
+    if my_sol['The number of cars in the dataset'] != solution_1_dict['The number of cars in the dataset']:
+        print("Sorry, but it looks like you missed the first one.  The number of cars in the dataset should match the number of rows in the dataset.  Try again!\n\n")
+
+    if my_sol['The number of car features in the dataset'] != solution_1_dict['The number of car features in the dataset']:
+        print("Sorry, but it looks like you missed the second one.  The number of car features in the dataset should match the number of columns in the dataset.  Try again!\n\n")
+    if my_sol['The number of dummy variables in the dataset'] != solution_1_dict['The number of dummy variables in the dataset']:
+        print("Sorry, but it looks like you missed the third one.  The dummy variables are columns with only 1 and 0 values in the dataset.  Try again!")
+    if my_sol['The proportion of minivans in the dataset'] != solution_1_dict['The proportion of minivans in the dataset']:
+        print("Sorry, but it looks like you missed the fourth one.  The proportion of minivans in the dataset can be found by using the describe method on your dataframe or directly on the minivans column of the dataset.")
+    if my_sol['The max highway mpg for any car'] != solution_1_dict['The max highway mpg for any car']:
+        print("Sorry, but it looks like you missed the last one.  The max highway mpg in the dataset can be found by using the describe method on your dataframe or using the max function in numpy.")
+
+    if my_sol != solution_1_dict:
+        return display_gif('https://bit.ly/2Hog74V')
+
+
+def check_question_two(solution_2_dict):
+    a = True
+    b = False
+
+    my_sol = {
+        'The components span the directions of maximum variability.': a,
+        'The components are always orthogonal to one another.': a,
+        'Eigenvalues tell us the amount of information a component holds': a
+    }
+
+    try:
+        if my_sol == solution_2_dict:
+            print("That's right these are all true.  Principal components are orthogonal, span the directions of maximum variability, and the corresponding eigenvalues tell us how much of the original variability is explained by each component.")
+        else:
+            print("Oops! That doesn't look quite right! One or more of the statements you marked False is actually True. Try again!")
+
+    except:
+        print("Oops! That doesn't look quite right! One or more of the statements you marked False is actually True. Try again!")
+
+
+def check_question_five(solution_5_dict):
+    a = 'car weight'
+    b = 'sports cars'
+    c = 'gas mileage'
+    d = 0.4352
+    e = 0.3061
+    f = 0.1667
+    g = 0.7053
+
+    my_sol = {
+        'The first component positively weights items related to': c,
+        'The amount of variability explained by the first component is': d,
+        'The largest weight of the second component is related to': b,
+        'The total amount of variability explained by the first three components': g
+    }
+
+    if my_sol == solution_5_dict:
+        print("That's right!  Looks like you know a lot about PCA!")
+    if my_sol['The first component positively weights items related to'] != solution_5_dict['The first component positively weights items related to']:
+        print("Oops!  Looks like you missed the first question.  Notice that there are two bars that are large, positive, while the rest are mostly negative.  What are the two bars related to?\n\n")
+
+    if my_sol['The amount of variability explained by the first component is'] != solution_5_dict['The amount of variability explained by the first component is']:
+            print("Oops!  Looks like you missed the second question.  If you look in the table, you will see the variance explained in the first column.  Then the principal component is provided as the weights that show up in each associated row.\n\n")
+
+    if my_sol['The largest weight of the second component is related to'] != solution_5_dict['The largest weight of the second component is related to']:
+        print("Oops!  Looks like you missed the third question.  If you look in the table, you will see the variance explained in the first column.  Looking at the bar chart, you can see that the largest weight for the second component is the blue bar on the far left.  This is the first column in the original set of features.\n\n")
+
+    if my_sol['The total amount of variability explained by the first three components'] != solution_5_dict['The total amount of variability explained by the first three components']:
+        print("Oops!  Looks like you missed the last question.  If you add all of the variability explained in the first column of the table, how much is explained by the first component?")
+
+
+def question_check_six(num_comps):
+    if num_comps == 6:
+        print("Nice job!  That's right!  With 6 components, you can explain more than 85% of the variability in the original dataset.")
+        return display_gif('https://bit.ly/2cKTiso')
+    else:
+        print("Oops!  That doesn't look quite right.  Try again.")
+        return display_gif('https://bit.ly/2AC30ww')
+
+
diff --git a/python/Unsupervised Learning/Random Projection and ICA/ICA mix 1.wav b/python/Unsupervised Learning/Random Projection and ICA/ICA mix 1.wav
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diff --git a/python/Unsupervised Learning/Random Projection and ICA/ICA mix 3.wav b/python/Unsupervised Learning/Random Projection and ICA/ICA mix 3.wav
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diff --git a/python/Unsupervised Learning/Random Projection and ICA/Independent Component Analysis Lab.ipynb b/python/Unsupervised Learning/Random Projection and ICA/Independent Component Analysis Lab.ipynb
new file mode 100644
index 0000000..4f29876
--- /dev/null
+++ b/python/Unsupervised Learning/Random Projection and ICA/Independent Component Analysis Lab.ipynb	
@@ -0,0 +1,533 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Independent Component Analysis Lab\n",
+    "\n",
+    "In this notebook, we'll use Independent Component Analysis to retrieve original signals from three observations each of which contains a different mix of the original signals. This is the same problem explained in the ICA video.\n",
+    "\n",
+    "## Dataset\n",
+    "Let's begin by looking at the dataset we have. We have three WAVE files, each of which is a mix, as we've mentioned. If you haven't worked with audio files in python before, that's okay, they basically boil down to being lists of floats.\n",
+    "\n",
+    "\n",
+    "Let's begin by loading our first audio file, **[ICA mix 1.wav](ICA mix 1.wav)** [click to listen to the file]:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import wave\n",
+    "\n",
+    "# Read the wave file\n",
+    "mix_1_wave = wave.open('ICA mix 1.wav','r')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's peak at the parameters of the wave file to learn more about it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "_wave_params(nchannels=1, sampwidth=2, framerate=44100, nframes=264515, comptype='NONE', compname='not compressed')"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mix_1_wave.getparams()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So this file has only channel (so it's mono sound). It has a frame rate of 44100, which means each second of sound is represented by 44100 integers (integers because the file is in the common PCM 16-bit format). The file has a total of 264515 integers/frames, which means its length in seconds is:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.998072562358277"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "264515/44100"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's extract the frames of the wave file, which will be a part of the dataset we'll run ICA against:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:3: DeprecationWarning: Numeric-style type codes are deprecated and will result in an error in the future.\n",
+      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Extract Raw Audio from Wav File\n",
+    "signal_1_raw = mix_1_wave.readframes(-1)\n",
+    "signal_1 = np.fromstring(signal_1_raw, 'Int16')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "signal_1 is now a list of ints representing the sound contained in the first file."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('length: ',\n",
+       " 264515,\n",
+       " 'first 100 elements: ',\n",
+       " array([  879,  1268,  1460,  1756,  1943,  2216,  2407,  2668,  2866,\n",
+       "         3106,  3308,  3546,  3752,  3981,  4175,  4395,  4588,  4790,\n",
+       "         4966,  5146,  5292,  5436,  5550,  5643,  5717,  5759,  5790,\n",
+       "         5798,  5789,  5756,  5713,  5649,  5576,  5478,  5381,  5267,\n",
+       "         5146,  4999,  4856,  4682,  4502,  4308,  4097,  3875,  3637,\n",
+       "         3380,  3107,  2825,  2514,  2194,  1847,  1472,  1087,   671,\n",
+       "          227,  -219,  -691, -1176, -1666, -2167, -2669, -3179, -3668,\n",
+       "        -4170, -4643, -5116, -5559, -5985, -6380, -6765, -7105, -7422,\n",
+       "        -7706, -7955, -8163, -8339, -8470, -8557, -8600, -8618, -8585,\n",
+       "        -8524, -8425, -8298, -8129, -7947, -7720, -7475, -7205, -6916,\n",
+       "        -6606, -6266, -5922, -5556, -5165, -4774, -4353, -3922, -3476, -3021], dtype=int16))"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "'length: ', len(signal_1) , 'first 100 elements: ',signal_1[:100]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If we plot this array as a line graph, we'll get the familiar wave form representation:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f544220ada0>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "fs = mix_1_wave.getframerate()\n",
+    "timing = np.linspace(0, len(signal_1)/fs, num=len(signal_1))\n",
+    "\n",
+    "\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Recording 1')\n",
+    "plt.plot(timing,signal_1, c=\"#3ABFE7\")\n",
+    "plt.ylim(-35000, 35000)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the same way, we can now load the other two wave files, **[ICA mix 2.wav](ICA mix 2.wav)** and **[ICA mix 3.wav](ICA mix 3.wav)**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:6: DeprecationWarning: Numeric-style type codes are deprecated and will result in an error in the future.\n",
+      "  \n",
+      "/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:13: DeprecationWarning: Numeric-style type codes are deprecated and will result in an error in the future.\n",
+      "  del sys.path[0]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f54421ef390>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f54421a1f98>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "mix_2_wave = wave.open('ICA mix 2.wav','r')\n",
+    "\n",
+    "#Extract Raw Audio from Wav File\n",
+    "signal_raw_2 = mix_2_wave.readframes(-1)\n",
+    "signal_2 = np.fromstring(signal_raw_2, 'Int16')\n",
+    "\n",
+    "\n",
+    "mix_3_wave = wave.open('ICA mix 3.wav','r')\n",
+    "\n",
+    "#Extract Raw Audio from Wav File\n",
+    "signal_raw_3 = mix_3_wave.readframes(-1)\n",
+    "signal_3 = np.fromstring(signal_raw_3, 'Int16')\n",
+    "\n",
+    "\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Recording 2')\n",
+    "plt.plot(timing,signal_2, c=\"#3ABFE7\")\n",
+    "plt.ylim(-35000, 35000)\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Recording 3')\n",
+    "plt.plot(timing,signal_3, c=\"#3ABFE7\")\n",
+    "plt.ylim(-35000, 35000)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now that we've read all three files, we're ready to [zip](https://docs.python.org/3/library/functions.html#zip) them to create our dataset.\n",
+    "\n",
+    "* Create dataset ```X``` by zipping signal_1, signal_2, and signal_3 into a single list"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(879, 157, 879),\n",
+       " (1268, 899, 2584),\n",
+       " (1460, 1610, 4081),\n",
+       " (1756, 2325, 5682),\n",
+       " (1943, 3022, 7147),\n",
+       " (2216, 3718, 8689),\n",
+       " (2407, 4386, 10114),\n",
+       " (2668, 5056, 11583),\n",
+       " (2866, 5690, 12954),\n",
+       " (3106, 6318, 14327)]"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X = list(zip(signal_1, signal_2, signal_3))\n",
+    "\n",
+    "# Let's peak at what X looks like\n",
+    "X[:10]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We are now ready to run ICA to try to retrieve the original signals.\n",
+    "\n",
+    "* Import sklearn's [FastICA](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.FastICA.html) module\n",
+    "* Initialize FastICA look for three components\n",
+    "* Run the FastICA algorithm using fit_transform on dataset X"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# TODO: Import FastICA\n",
+    "from sklearn.decomposition import FastICA\n",
+    "\n",
+    "# TODO: Initialize FastICA with n_components=3\n",
+    "ica = FastICA(n_components=3)\n",
+    "\n",
+    "# TODO: Run the FastICA algorithm using fit_transform on dataset X\n",
+    "ica_result = ica.fit_transform(X)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "```ica_result``` now contains the result of FastICA, which we hope are the original signals. It's in the shape:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(264515, 3)"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ica_result.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's split into separate signals and look at them"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_signal_1 = ica_result[:,0]\n",
+    "result_signal_2 = ica_result[:,1]\n",
+    "result_signal_3 = ica_result[:,2]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's plot to see how the wave forms look"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f54325fc588>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f54325a6940>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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8pKONMfsaY0a2NE5VmtxFq4nf8yYAiYmfEPvjSzhTdOBHJYlcPZ7IDycUO4y8SfZLd95bgFsmt+hzEbvzZSJX/rPYYZSM2EPvNFrGnbUM8LqTRL53D4kPcuvrnSuzdkuLj+F+uToPkRSf8958Ev/WGTLrit7wNDVjxuGuqZzPokqUj5btg4AFxpgvjTEx4HHg9DplTgeSox6eBo4VL2fN6cDjxpioMWYRsMA/nmojnM+WppaT/1hMBX5oGGOoGTPO+1BcsbHBspGf/4tEji1rqnU5M5fUeh792WNEfvM07rqtRYqoZRJT5xG9YyKJSbNwZ39d7HBKSnrrdvy5adT8cDzOJzuuv5uhIuxM+7JVYmuK+INvE5vwn2KHkVc1lz9A7MG3ix1GSSmnDDRtUT4q2/2ApWnPl/nrMpYxxiSATUD3RvY1wOsiMkNELstDnKrEmQqeBc2kVbDT/2FnLLtqE/EcWtVKQVvr8uN+VX+wnFmylvj/vVGEaFoufs+buJ8t9ab7zsJdtYnYPZMxidJ/fxZqMF3i3zNgUw3xx9/DbNxG7L43if3ppdxiqolh1hf3y1jdvNXGdVODEePPfEjkxw/jrt2CicYxsQTOJ0tK+70diWvqu7q2RXFXbSrrtJWVLB8DJDNlVa/7Ls1WpqF9DzPGLBeRnYBJIvKFMaZeDcSviF8GMHDgwNyjViXHnV56rUJ5k2XUuDEGogmkKtjKAbU+E0sQf2AKwXMPQbq2L3Y4zeLOz5xuq5KyArhfrcMa2D31PH7/W7jzVmIfNRx7tz4tPr4xhvgj/yVw6DCsob1afLx0yZzNhWJWbCRyzcM5lU18sABrp07E7n4ds25r44MsCyz290k4Hy4keMWxuHOW47w9h9ANZ5B4wcuqE/3Jo7XKB39wHNagHrjzVxL4xu7FCFkl5fjFJ/rzfyEDulP1u7MKHJBqqny0bC8DBqQ97w/U/cRLlRGRANAZWN/QvsaY5M/VwHNk6V5ijLnXGDPSGDOyZ8+eLf5lVAkwYDZsw5mxqNiRNEujLUJp250pc4hc/gDuqk1Zj2NcQ+yxqbgrG+5+UhRNaPxypn2J8/4C4k++X7h4Csz1p5fOxmyNELnhqYzXs1zE/vZa5g35aumMOzhvzCL6hxfyc7wS4k77ksjNz1IzZhzxf7xB9KZnMSXSxcj5cCEA8XGTU63CiZc+yb7Dxm1Eb3yG+P1TWiG63LXFadyb8iXSNJCqUhVPPirb04BhIjJYREJ4Ax7rfoq+AIzxl0cDbxqvJvECcK6frWQwMAz4UETai0hHABFpD5wAzMpDrKrEZBsAFPnts8T++hrGrZwWw6TEE++T8G/rxp/zEu2YTBXprZHUNue1T4n9JUslqNyU8N3plnKmfYn5ah2JlxuoxJSIbDP1ma1RasaMI/rX1xrMMd38E1fwHwBgFmYekFgzZhw137+vlaNpmPvx4oYLRHZ0yzHbo9pFQalmanFl2++DfTXwGjAHeNIYM1tEbhaRb/nFHgC6i8gC4Frgen/f2cCTwOfAq8BVxhgH6AW8KyIzgQ+BicaYV1saqyotsXvexHn7i3rrEy9/Ahu2eU/K8f9yppjrpIuLJwcsJVPiORl2Sq6K+tO+l2QlJfeY3MXehCHuvBWY7RWaYs6/Ru6iNSQmzcK43sDY6F2vFDmw+rJWnPz0f+6MRUR//RTu16U1O2JZizsk3ptPzdUP4S5Yhbtsfck2KMT/9V6t55Ef/JPIFQ8WKRqlylteJrUxxrwMvFxn3W/SliNAxk5ExphbgVvrrPsS2CcfsanS5Uyd12gZ9+PF2COHtEI0hRW96+UGt8effB97/0EZB09Gb/JGmZssWUxMNE7ksgcInD2K4Kn7tTzYpmhCbmHn9c8AMOu2Erv7dcLXnVaoqFqd2bCtVr9ts2Qt8SXv4n7pDUJzGxkUW9Lq5N52PluKtWtvJFz54wwKIT5uMgDRW55LrQtedgz2gUOIXPsI1tBehK4+AQna2Q7R6qJ/qd3W5a7ciHRtr38DrUBn0KwMOl27apDxuzIUi1OWgyYzVEA3NTyrXbIinette7Olhpox47xuC1u9ylBi0iycaQtJvPU5ZuN2on95lcS7c5sWehM5/2ne8d3PKyzN3IZtRH/7LPHxtVOsOVPnFymg/HM+XIjz4UJid0zMT3/ruJP3vNTlKn7vm0QuvR+2RHA/WUL0un8VO6Ra3I8W13oeve5xYn/Wm82tIf5Q09M2Fjv7japPK9tlxPlwIY7/oWeMIf7UBxlzveaDMYbYuMlErnqoIP8Q3VxnN8vjHVZ30WqMMRjX4C7fUGsgY+RXT9ZrvWmO+NMf4n7S8CC6bIwxmLTUcmbd1qwfmvFnvJnUYv+YhCRz+mzYRuxvk4g/9A6xeybjfrSY+H1vNSuWnGPWGQdTklN9Vypn8mxif58EgFm0plnHqLlmApHLHkg9j//DS5noLllbcjMwFpNZt5WasfcWO4yMkgMU3c+/xple3EHs0T88j/PF8orKBlRX8u5YU8Qff6+iX5NypJXtMhL7+yRif3mV2ANTSDw7jcRLHxO7+/WCnMt8uRrnPa9VrhDptHKfuCY//4CdWUuJ3vQszhuziP3pJaK/eILEq5/uOMuy9fVab5oj8eJHxJpZaXfenpPKGACQmPgxsSyV5dSEG67ByZCOzkRa6dZjC/qRJytXJhqnZsy4ip+kouTyyEumzKtNY1wXd533hT/x3vzGM+Zs3F5vVfyVmUR/8zSJV/IwqLQkxzU0U6L0K0uxu71B25Ebn8lpxs18c79YQewPL5D49/RWP3drMSubntnI+WAhjt41Kila2S4D7vINOGkpx5x3vkjlRs2Wv7klore/SPTmHf0J3a/WErnpmfz2HcvxH71xDZEbn2lSd5LoLc9Rc/VDtY+zxqsQuEvXp7owNDoSv5XVbSUyhox9ouu1AG6qX4Fhy45uK8m+ofF/TSX+r6n1juXMrD2BRfyFGUT/WjvzibtwVd5bsRMvfoS7bD0xv3XTeXuONwFIpt+nAkRKLBNFPiSe+pDotY/ifLGc+LjJRK97vOnHeNwbiJd41rtb4y5Zm6rAp4v+5VXiL37U4LGK3e2tLTIbt2MWr6k142Zr00G8GWzTzDGlJC8DJFVhRX/xRPaNBWjJqdufNpnKyp23EnuvAZl2KRjXn/44Nm4ywUtdiCYIHLFjgoXYY1NxXvuUqr9ehHRu5+2zIPttN3fWjglL3bkrqPnhBKr/elG9csYYiCUKOgAoclPt6XXdz5bWLmAM7hf17yqkt3576n9xSX65gB2vR7IlP3jeoTuO9fqnxP/1HqGrjsc+aKhXzu+iki5683PIzj2ounl0vRiby/nv3FQFKymZ7SA5AYiJJTArNyI9O+EuWNXqf3/p8jGjXs2PHkZsi8DJ+2Dt2htrYI88RFY8jv9+ytb65i5agwzqgeTy5Trhel/q/S4qdSeBcT9ajPvRYoKn7Z/1EPGnPsgtcJU3kWsmNLjdOC7UxJAOVa0UkQKIP/IuiffmEf7hSbgLVmK2RJA+XTCrN9f6H6pah7Zs51GqH3UrTmJglq2nZsw43IVN79eVSeTnj2XdFn92WvGm8I07xP/xBvEHpqS6HSTenoPzmleBdD5eTM0Px9eraDvzVuB8thR3gdfVot4EE5u2E5/4ce19PllCfPx/iFz2AInJs3BmfkX0jol5n6660X6vWV7r9C8MuUqfZMWZs+PLVLLPv5sl0wlAxB+sleyTbIwh/vInWfM058qsyt6VyKzfiok7RC69n+gNTxP5n/HE7piY6sNuHLf1c/42Msg1Jxu2YdZuIf7wu0RveBrwcq3XjBlXdn2W3dWba40xSEp2fXKmLSR60zOpQaK5fHakvyfMhm2YzTW4y5vQallmr2GlMdu9HO2JtFbu+CPvErnqoYJm1TAbtxP93b+b9JnkfrWuYGOeSoVZuJrEW58Tu/t1byzPH14g/sCUYofVJmnLdguZjduIXPMwoV+djtgWiZc+xv1iOeEbzmzVOKI3P0f4zguwunds0XEarAB9udqbQU8Ea+8BubVWFUDi+Rnez7RKsvOfubCphti9k1PrTMIhduvzjR/vyR2tYe6azcTSciLHJ7y743hL1mLah2FrFGuX/E4znUm2jB31MoDkcBnSW81jt71I8LJjsIb1hmQmk2enETh5n1otze7CVVhDe9VrtTSL15J44n3cWcuw8jB9dyaRHz9Se4Xf39nEEggQv+9NnPcWtPIU2IWpyCX/nuOP/RezaA2hX3qfJXVF75iI9OxIaMwRBYmjqaI/y/zF3Hl3LjVpWXASz3yIM/3LJo+JiPzoYagOQU2s6FOdq9xEfvBPABKvf0bg6OGA138Y8LLPfLgQsyVC8JR983pes3AVBoj+6SVClxyFNbjx2aSjNzwF1L+DUmkquT97OdGW7RZy/MGDiVdmpvo5F2sUcPTaR0nkkLu6JWJ3vULszpcbnba6MSZDn8xcJSZ6A6nMhh19e5Mt2ulfFqK/fqrJx47+NHvLfvTm54he9zjRW57DXbnRa101BrNpe2o5rzIMcsw8VXHjte34w+/Weu7OXEL0Z4+lBsECOFM+J/HKzNTz9H77qf3WbsH9ym/hjsRafUBa9LrHvZSH72Uf/BOb8B/iT3/gdUGJJTBbanBzHpDbkPx/uXTmr0y9hs6kWd7fcZbWOfezpThvFq9fbEPcudkHUZt1W5s/+DjD3YvIjc9kKOjfsdmifbZLQiRG4r/zvM+rtLEe8funkHji/YKd1ny1LjUvQdYyxpD4T/3J1NqS6F9eTY3BqRkzjtj9hc1apbRlu+X81t1a/0y2R4k9MIXgBYchVUHM1ghmSwSrT5eChxO/500Sz07H2n8QofMPbXyHNCZDpoCsZVvYhSC9xbjZYokGN2ebBCYf6g4Es4/cg+DF3yjY+RoSf6Tpr2WqtSmNySH7QfQnj6Y9SZD494wmnzufTCwBtoXYljewMhTAmTwbgMTk2bA9BqEAxBJU3TsWauJIl3bNO1kBbuQkBwfWUoYZNQqdTzz2zx2ZasziNRhjiFx8D/Yhw3Dem0/wkiNxZhQ3DZ3awazfRvzeN2uvS6t0J/z3aKE4ny3NOr7DeX8B8fun1FrnrtmMdO+AWG2j/dH9aDGRK/+J9PDuhDv/mQvfP7rIUVU2rWwXgFm1GWfVZtxZSzHrt7X6rVCzZjPOa5+S6NMFa++BWN075LRfYwNd0sUfmIL06QLiDY4KHL5bc8OtCM7bcwicXN6Tnja1xcnkmiu9gCKX3o/07ET4T+cR+eEESK9Ib/dbRf0vZdHfv4BZvIbg2KOIP/MhVbechfPxYgJH7pHTuXL5MtJUmQbzmkgc563PsfcZ6E1KFLCzXhtjDGbNFqydOjV4ntg9k3Gmzi/bW+bOlDm1nhu/H3fyzkz8wbeRni3rQqcKK/rzHRP1xCc0faKWpojdMTHr37pZXHusjLt6M9GfPUbg9AMIfvvAgsZVakxan/X4s9Ow+ndLDZRPiv3zbdzZy6i644LWDq+iaGW7gMz6bd5CloFc7prN3pS3gfrT8poN2zDROFbv5reGxx96B+nblfBN3ybx4kfYBw/D6t+t2cerK/a7f6eW3U+/wmyNEBx7dM6V+0oTvb7pac9KnVMGMz2aNZt3dH9p4O5M8p9scoBQ7G+v485dgXRtT+LNzwldeRwSyv6R6LwxK28xNySZfSjbcDL3q3VIjw5IuzDO1PnE732T0HWnYQ/vl9puttSAJVi79wVTv+XZOG6t9JDlJvrLJ+utS8/Ao1QmzrwVteZXAHD8rpcNdYVqC5JjR6p265PK7AX1v+iq5tHKdityPlsKtoU9vB8mEif608ewDx1G6PJj65WN/OhhoOWDN8zyDSRe/Dj1CP/uLG+wmW3hTJ1H4tVPqXrg0tSt9+ZKdkuI3fpvrF16Y+0zMHUbUXb20puFf3Nmxi8WqnTFbn+x2CHkpDn9QJPdpuLj38Gs3Yoz7Uvcz5cR/O43kKr6KR8LmU2hKaI3PIV0a0/VXd9NZSEyX6+H4f1wl29IDfxqSPyxqa325UGpYjIJB3fRGuxhvTMOmE885w8gtG0S73xB/IEpVP3lIqRLO5xPv0I6VCG9OiMe42zwAAAgAElEQVTtww2ex128BunSDunSvhC/Rqtxl6zF3ntgvfVm03bM+m05DT5tjEk4mOUbkQ5h4i9+RPDCwzMOCq8kWtluRbE7JgIQ/uN5JJIp66bOp2bqfOhYhdWrM6FrT8n7RDWJtIkgMg0ajD/0Tv0MF81k1m3FWbeg1uxVyZRxkbHepB7BCw7Ly7mUapnafaMTz0/HrPLuNjnvLyB07SlYfbsC4Hy0eEe3lBJg1m8j8fYc8CdxMZE48Vdn4rzd8MCvZBo9Z1r9PvtKVZLYhP9gHzKs1h3YBhmD8473/nGXrsP59/R6E/U01PgVvfEZqApSfc/Y1Drns6VYA7rnPE7Emb0Md8EqgqcfkFvMBRD735cJ3zwaEk6tQfKRXz8Fm2ta1ABoNtfgzluJ8/kynMmzkf7dMMvWY+87CHuf+hX8SqKV7ZZqxqCp9L5rKVsiuFsiRK78Z63VzrTcZ05srnxVtHMVf/S/rXo+pTJJZq4xa2vnXnc+XoJZs4XExE+QnTph7z+I2F9eLUaIDYqnTW+fePrDnPZpcIIspSqIM3l2k+7YpqdaTTw/A3f+ynplYo9NxV2wktBVx2dOsxuJ467ejPvFcuxDhxG7YyKyUyeq/nR+TjHE/vgSQFEr2wDR3zxdf2WWpAimJkZi8mwCp+yLWA1XiKJ3voxZtCY1vsIkswcZg7t6M9ZOnXCXb/Am31m8FhnYvWJavLWyXeJif3u92CEo1SakKt/+wE937grMu3Nxphf+C69SqnRkqmgDqUnUotc+Svg3Z+Ku3gxbI1hp3S6S+eeT8xOY1ZuJPTAF550vCF17CrE7Xyb8u7OQjlXerLgjhwC107om3p2LffAuXoalEmNqYkh1CPDmYohP/AR3xiKs3p2RHh2xBmXvZmJW+5+xyfEV/u/nfLYU565XsI8fgTNpFvaRe3hJB07Zl8BZo0Ao2rwe+SJFmxGwAEaOHGmmT2/dBO6JDxYQ/8cbrXpOpZRSSpU/2blHqqtlWWgfxtqjH9REcWenDaDv3A42bSf0wxOhUzXW0F4QiUF1KFVRzjxPBKn0rNnYR+5BcMw3cN76HOnfDenZ0RvzduQehC4u7iRfIjLDGDOysXLasq2UUkopVQRlVdEG2BbFzXS3z2+lTrw5G3fWslQrdfD8Q7GP2RMa6g7SyJwZzttzcN6unxXFeetzaqZ/iXSspuoP5zTp12htWtlWSimllFIt5s5aBngz4oKX+Sj+2NTCnXBLZEff7xJWGT3Pi6jc+xEppZRSSqnCyUtlW0ROEpG5IrJARK7PsD0sIk/42z8QkUFp237hr58rIifmekyllFJKKaVKXYsr2yJiA38HTgaGA+eJyPA6xcYCG4wxuwB3Abf7+w4HzgX2BE4C/iEido7HVEoppZRSqqTlo2X7IGCBMeZLY0wMeBw4vU6Z04Hx/vLTwLHi9b84HXjcGBM1xiwCFvjHy+WYSimllFJKlbR8VLb7AUvTni/z12UsY4xJAJuA7g3sm8sxARCRy0RkuohMX7NmTQt+DaWUUkoppfIrH5XtTCME6ybvzlamqevrrzTmXmPMSGPMyJ49sydTL5TE1Pmtfk6llFJKKVUe8lHZXgYMSHveH1ierYyIBIDOwPoG9s3lmCXBnbW08UJKKaWUUqpNykdlexowTEQGi0gIb8DjC3XKvACM8ZdHA28ab+rKF4Bz/Wwlg4FhwIc5HrM0xJ1iR6CUUkoppUpUiye1McYkRORq4DXABh40xswWkZuB6caYF4AHgIdFZAFei/a5/r6zReRJ4HMgAVxljHEAMh2zpbEqpZRSSqnKIX27FjuERonXwFwZRo4caaZPn96q56wZM65Vz6eUUkopVUpkp06Y1Zu9Jx2qCF19PLH/m0zg+BEknv6wYOcNnDmSwLf2R6zizNEoIjOMMSMbK6fTtbeQ9OiAWbu12GEopZRSShWcfdiuOP+dB0Dg1H1JTPyE8O3nAQazbitWz04AVP/1IszmGhLPzyBw2v4knp3W5HMFx3wDZ+p83PkrM28/o9F6bknQynYLWbv3xXl3XssOUhUkcPoBWP26ggimJobzxixC151G4oWPSDw/Iz/BKqWUUqpoqsdfQfypD0i89HGD5cK3jMZsjRK7/cVWiix3ocuOwYz5BmZzDVbPTgTPPtjfIohf0U6STtVU33+pt1wdJP7sdEJjjyL+3DTM1xu89b07Y1ZugqogROJYBwzGnbEIgMAxe2KP2oXIlf8keMGhxB+digzqiQQs7KPLZ65DrWy3UODU/Zpc2Q7/5kyiNz+Xem4fMozgKfvWPu6oXQAIfvvAiqpsWyP6485aVuwwlFJKKQCCFx5O/JF3cy5vHTiE0AWH4S5eg3SqJnbfW5gVG7OWD3xzPxIvfYz07+ad76xRWCP6E7stc0U69LNTsQb2wPmixJKwda7GGuSlWJZwEOkZbNLugRP2JnDC3oBXFzCrN2O2R2FLhNjfJ2HvNQBn2pfYo4YSuvTo1H7SPkz1+Cu85R6dsHbphXSqztMv1Tq0st1CUtW0P7bkHwwAnaqp+sM5UB3Kc1QlImBBwgVAuneg6s4LMZu2E/nhhCIHplTjgpcciTW4J9gWsfunYL5cXeyQmq5LO9i4vdhRKFXSpG+XHct9umA2bYftsXrlqv5+MdKhKvXc7tre+zlqKIl/zyB4/qHEH5tab7/gWaOwBvfE2qV3ap3Vq3O9coFzDgbXYI/wMh9bu/Zp/i/VAsGLj0B6d8b9YgWJf3vj4KruuhDp1iFv55DqELJzj9Tz6oOGYmpiSL9u2AcOydoH295/UN5iaE1a2W4FVeMuIXLFg7XX3XUhVAWRduEiRVUY4ZtHE/3N0wBU/XUMiYkfEzh+L8T/UJLO7ai6ZyyRyx8oZphK1VN13/eJP/g29jHDsev8k6u68ds481YQu/X5IkVXnwzuiVnU8Ky59oFDcCbNQgZ0x9qjL87rn7VSdEqVkM7tYNN2ZGgvrCE9cSbNqlckOPYonI8XE77mJACif34V9+PFhH55OvF7JhM4a1Stina6wCn7gmOwj9kzVdmuuv9SIt+/L1XGHjmk1j7SrQNV918KAQvz9QZkp05IqHaVTKxM8/sVVuj607D38Cbstvfo51W2hbxWtLOR6hDBM8ujD3ZTaWW7hTIlcwledgzxe98kcMo+BM85BIDA2aNw3vkiVaY1/nCLwdq5B1V3XYjz+ddI+3BaX64dmno3QKlCq7p3LBIKELri2GKHkrOqm75D4r/ziN/7JqH/OQHah1O3pYMXHY4z8ysQ75914PBdsU/0bt/a+wxEOrUjdv9bmCVrixa/UoVmHzOcwIl7Izv5rcgC7vyV9Srb0rkd9p79CRyxe2pd6OrjceetxN6tD/adFzZ4HgkHCY4+CIDAtw/0BgIGLMK3np15PuzkfkHb++l3LykmGdwTe++BqYp2UtU/vgdFqPRXGq1st5C087uApHWZCBy2K9aQnZDeO24TBU/dj+Cp+xUjxEZV/W0MxB0iP36kWfvbR+yONaI/1kDvlpB060Dg8N3yGaJSeWXt0ovAmSOJ/WkioWtOQsKNfwGU7h1bIbLcyMDugPdZEzhs13rbA8eOIHDsCGJ+K5sBRITQBYelygTPGkXsjomtEq9SRWHA6t2lwSLh334HK0NlVwI29vB+GfZoWPD0AwiefoB3jBKoRGdT9deLSEyZk8oQUnXTdzKWk/aVdfe9WLSy3UJSHaLqnrEQChD53j2p9Vafht/gBYmlb1esIT2x9uyPfcgwEo+/R+LVTxvfr6M30CB0/WlZB2xkEjhjJARtgt8szS8Rqok6VsGWSLGjyIvAOQeTeOJ9gmO+QXz8f1LrrT37EfrJqSCCWELV3WNyHmhjdS/83ajQT08lMXk27seL659/WG/Mtijh35wJdub+jMELDkP67ZjgQZINUm79W3DWiP75CLko7IN3wXl/wY7nh++Ku2wDZnHD3WpU5bP27E/o8mOI3jHR697RWHl/wF9bEfjOgdgjBiCd2xE4ejiJZ6dhH7VHscOqeFrZzoNkt4jA2aNqDYDIl+RI5pTqENT4gzf8AVDhP55Xb8BF8LxDSbz6KTKwO8FvHYA1rDeJVz4h8J2DkFCA2KP/TeXKBOrdPsomOPaoWrfbSpW1z0DcmV8V/DxVfxtD5OrxBT9PwUnTbxUmu0wVmz1qKM4HC6FjFVW3nQvtw6kMP4Fj9gTAbItCOICkVVRLaUR78OIjsPcagL3XABLvL0BCNibuEP/HGwCEf31Go8cInLBXnTXZr6k043qXitAPjqPGr2wHLzmSwJF7YLZHif7qScz6bUWOThVT6EcnIaEAVbeclXG7NbQX9pF74Lw9p5UjKz5r/0EEv3VA6rl0qib8x/OQVmhIaOu0sp1HheomEjxrFMGzRmESDliCWBYmliA+/h2C5xzSYIUhfNu5SOfq1EDM4HmHpraFLjgM0m4r58LavU9ZVLQBQhcf0eyuMY2pHn8FkWsfgaCNdKwmfNu5uAtXEb/vrYKcrzVYu/bGnb6o1rrgpUc3+DtJiWTSCY49CmvEAKzd+2YdxFSKt0NDPz0Va/e+uHO+xt57YGp94OBdUsv28H4ZW6ZzkvxeUUEzBSdZ++6M+8kSLzcvIO3CWAcMzjj4TZWYQmTJESF09fH1BhnWK2ZbhC45Eve0/bz+VW2ENbxfavBnrfUZsqKo/NPKdhmRgL1jORQgdOkxje7T1O4s2VIXJQVO2qdJx8vGPmL3WgNGW0VVEOnWAbN8Q9Yi9oFDsIb3w2zYRuKFjzKWCV55nHe4tEEzVp8umG3l3QUjdPERmLNGEb3u8dS6wOG77ahsd25HcPRBuF+uxnnr8yJF6bGPHk7wu4dDJO6NlA8Hy+ZLYDrp2REJ2rUq2vXKdGx+67s9cgiJl2di75X9+OUqcMJexD5ZUutuonRpX8SIVC6q7h4D1aFamTrywdqtT72MHw2WrzP5SqULXXtKsUNo07SyrWoJnLh31sq2feyeWPvunJ8TNdL6kBd1Br1V3zMW4xriD07B+c/cWtsCZ48icMiwVJYYk3CQ7h2xj9id6M3PplKs2ceNSE04VGmkY3XGil34t9/xvqh09yqGHLE7NUWqbEufLt7kEQHL6w5Sgq3VTdFYK1xLWUN71c7tX8aCFxxG/NH/pp7be/av97vZhwwj8dQHrR2ayiJw3iEkXp4Jm3a0Ykunakzcyd85TtnHO4dqUDLziSoOrWyrRkm/rlT9/pz8HrRQqYSCNqEfnYQz8yukfZjw784i+uunUpvFEoLfPRxrYA+svQdgtkSw+nSp1/VAAjYBf9BI+LrTMOu2YtZuwdqzfAeVpbMP2QV75FBid7+WtYwM7QVkHkAUvPI4Ek+8n7qF32rKuJ9xusBZo3Amz67YFKB1SY8OmLVbW3aMLu0aL1MZfx4VQzpWU/W7s3BXb8KdsRj7kGH+hpYd1z58V5xZy2Djdqzd+sLLM5Gd2lZLda6s4f10AGQJyDykXbVpVX/5bsHPke9k/aEfn+z9/Mkp2CMGpFKcWQO8FGnWyME7zh0OEjhhL6zeXbCH9c7axzdVvjqE1b8b9r47N9g6IKH8Vzzt40fk5TjSsxPB83f017d264s9cjDhm0dn3Sf8k+y3HQOjdvG60RQ4/2pw7FHezwsOw9p7AHaGNHelKnDGSMT/+6sr+M39vImtKkjGNGcdqwj/4RzCvz8HK23mt+Blx3g5iBsStAmctDchv5+pDO3lvR86N17pVq0vfNu53kKHKsK/Pxv7hL2wRw1FOlVj79Kb4DkHYw3M/H7IlbWP1x3KShvMbw3sTuiakwhe2LTxR22BDN2J8HWnVezd2HKiLduqnvR+j9K7M8EmDqLMSZ4qaVX3jE1lg6k7lW6qzLhLWqXbSkv/kWRijxySlwFf1m59CJy4N+7X63He/iLVsmSlTZdbVykMKLT33ZmA31UgcMJemI3bcd6eQ+D4ulk3SosM7E7wzJFIt/bEH3y72OEUnPTvRtWtZxO95TncBasA70t7+mdJ+JqTqLnkXnBcrxKWNgYleMWxYAlWn65Eb/DuRFXff2lqe7K7SOjCw+HCw1vjV1I5Cl58BNK1fWqW4OA5B2P161Yrp3s9zbwFEb72FMzmGqRTNVa/biRe/xS6tMfev23cIWqK4KVHl+3U5pVIK9sqI/v4EdjD+xfuzZqH+73SrX2t2SizZqEoQsaMuvmdc2Ht3hd3xQbYVJNaZ+/et9H9wnecT/Snj9Ve2T4M26I74jnvkOz73zwak9anMnzLaLCKe9Or6h/fw124ql6mHenSjqo/nV+kqHKXmrGujsCp+5KY+EkrR5M/wYuPIP7QO/XWW3t4f6fhG87E+WQJ8RdmQKfGW6CD3z8Ks2w9gWT3ghaqpKQr1h59cecsL3YYjQocPTy1nPP4gBZ8/Cc/E6zBPQldXj4zvram4MVH6MRyJUYr2yqjUKFbjzJVtm0LHDfrLlUPXEpk7H1eJXtIL0I/KN0P2lz6l1p7D8D9dOmOFTnUFEI/PRXp3blW5Vo6VSNDe2EWei2KgbNGYY8aWrtM6otI/de9but2cibQfLP2G5RxshYAbAv7mOGpVnxpH24wQ0epso/dE3uPvlgjBmTcHjz7YIJnH9zKUeWHtUsv7FFDU5Xt0PWnYTbXYA3oXqu/rL3vztg5DqQOfKP8Msi0BvuI3QmOPojIDycUO5SMqu4eg9lSA9FEsUNRvvQ0rfbB2m2k1GhlWxVHhrq2DOyeyvqRzhrWm+BF30ACNlUPXe6VrYCRUOGfnErNmHGp59K9A4Fde5N40ZvAKHhR/S889l4DMOvrDDSzLUS8lLGhG87ArjOxUuhnp6aWg2cdBMZgH1rgvs/hQL1/xKHvH0XkqoegXQi2x2ptq37wMgASfbtSrkLXnIg1YkDWDCO5zGZXykLXf6vWmIVcJ8FqKunRkUAzZ6Ut648FEe+9edQehL53ZLGjaZTVryVTkZfzhSo90qdL7TStAc08UmpaVNkWkW7AE8AgYDFwtjGmXhJjERkD/Np/+jtjzHh//QHAQ0A18DJwjTHGiMhNwKVAsub1S2PMyy2JVZWWwLEjUpVKa+QQ3OlfZu3HnT5zXtlUso3XyulMng14fVrNsvUN7hI8+2DMpu2p1wW78Q/M4PmHIgGb4BXHknj1U6whO6W2hW85CzC1WqqlYzUhf9BhIdlH7F6/r7lfCbUP3RXnjcz90JOzPZYje//B2bcdsTvBc8qzRTv0PyfifrU2VdEOXXda81MWdqxqdDKTqv+9oHnHLnPh35+N9OjYNipKTfgYt48fgfPOF3mb46ESVfmDU8O3no2piWmavxLU0o6Z1wOTjTHDgMn+81r8CvmNwCjgIOBGEUk2X/0fcBkwzH+kT290lzFmX/+hFe0KkxxMAxD6wbFU/fUipGv5D3Kx9huUcX1VY5kXqP2aePxuJXUHKobrZz2xenYi9N3DkbS+1tbA7gXrEtIcEgpQNe4Sghcc2nhhVTT2wbtgp2UvsEcOJvjtA3c8H94Pa5dezTp2+FdnELzkyFqDI9u60I9Ppnr8FVh9uyKhQN4zNeUqmekjG/uI3XdM693CEJvSaCKd21F97/dr/Q22Jdbw3O8gWf27YQ/r3XhB1epa2o3kdOAof3k8MAW4rk6ZE4FJxpj1ACIyCThJRKYAnYwx7/nrJwBnAK+0MCZVJgLf2t9LpxewoXM77D36ei3cZSw1YDPQzO+xGf4JWX264C5YRei607wi7cOpVnPpVvoz5ln7DExltEkOVg2OPQprqNcKb7aU98ybANbufYodQv60DxO66BvUfLAg74e2duqEpfmQU0ppwqHwtafU6taWZJ+4N85rnyIdwoR+8S3cj5e0aFZT1USNfPmyj9RxD+WgpZXtXsaYFQDGmBUislOGMv2AtFFgLPPX9fOX665PulpELgKmAz/J1D1Flbfgdw6q9dw+dk/clRtrdT8IXX1Ca4fVIsHvHo706YK110CcmV/l5Ziha07C+fQr7LQWjuCFh2PvNwhrROlPsiPtQli9amfnKMep1bORnTplnQrZPmQY7hfLCY4+KOP2YgtdezLEHQjaxO7Udo42qV2Iqj9nmFtBIHTV8Vj7DUKqgwRO2RcJB7FOaN20m+ld49oia7c+uLOWNVCiTLpWtnGNNr+JyBsiMivD4/Qcz5HpL8E0sB687iVDgX2BFcD/NhDfZSIyXUSmr1lTf3CdKh8iQvBbB9S6RW0fOKSIETWdtA8TPP0A71ZwWiu1yZJpJHD2qNr7p02CYu3l3daVTtX10jiJJdh7DSh6H/ZCTzdeDqx9BiIZuvaA9/qELj8WKdGJWOx9dsYeOQR7nx3ZQ+y0rlDWbhXUYl9AwUuPxto199cqfPNoqu4eU8CIsrMOGAzp2ZICdurvN/yn85Ge3p2H0E9OxT7Qy4cePPPArH/jhRQ4aW/sCpm1t9kaScNq9SvfQeVtSaOVbWPMccaYERkezwOrRKQPgP9zdYZDLAPS82D1B5b76/tnWI8xZpUxxjHGuMB9eH29s8V3rzFmpDFmZM+e9aeVVuVFOlUTvuHMYoeRH2n1YBHxBofVLVKn76pYQtW9Y6m660Ks7qXfh10GZ3jPdW1P4LgdM19mS4NXKews/fTLlTXAyzIRvv1cQg3MItqWVd07ttZze+SQnNKtWfvuDF3aIX261Msh31qkOlR7foK0zyVrp05Ir9Lp5hM8T8d3NErHP5SFljZLvQCMAW7zfz6focxrwO/TBkWeAPzCGLNeRLaIyMHAB8BFwN3gVdyT3VOAM4GWT6Gnykr4pm9DmfcLDH5z/1pdYqRr+3r9k+2jhxN/bCqBtG4GEg5mHARZitJb1sN3nI/YFtLN+5JQPf4KzLZoScxEmXedqrH36Ifz0aLKa3kLev8WrN5dihxIM2SZ2CqfpGdHJBwkfMtZqdkuc1F1/6UllyUicPI+BOp0C7F27oE7axnSubw/fyuFPWooiac+yL59ZPYsSKp0tLSyfRvwpIiMBb4CzgIQkZHAFcaY7/uV6luAaf4+NycHSwI/YEfqv1fYMTjyjyKyL163ksXA5S2MU5UZa3AF9NOrU8kMHDWc+ITas0pKKFBSg6RawupZv0WsIivaQHWRugAUUvj2c3HnrSzra1bobk32qKEE/VkLrYHdvXSWsQQI2IfvirtgJc7U+V7hLu1SaQ5lUM9mVbStvQbgfra08YJNZB84hMSLHxP45n71Zt4NfOcg7JFDSiqTUVuW6XM1Xal2UVO1teiTyRizDqg3jZ8xZjrw/bTnDwIPZik3IsP6DKM1lCozdu1eWoFj90R6dSL2p4mEf994KkClWpPVu0t5tma3JttC7NrpNd0Fq0Ak1T+/xq9sV916NpGrHsI+fkThZ+TNlW0ROG4EsnMPAifvm/GLldgW0gqDEq1de+POW1nw8yhVCnR0k1IFkilfrj1iQMW0ZCeFrj4e2alz4wUrQNXdYyDLYFdV2aR/NwKn7V9rXejaU3CXrqvXoi79uyEdqqi660JoSctjHsc/B04/oHau6iLfwQj/6oyMqQZVfdbIwbjTF9VbH7z8mCJEo5pDK9tKFVD49nOLHULB2QcOLXYIraZYg9pUcQWvOJbAIcPqrZf2Yezd+9ZaV/XgZalKcnL8QjEFrzyOwKjGB2+WEvv4Ebhzlhc7jJJh79EvY2VblQ+tbCtVQHpbXqnyl6minY3YLZ2YOU2F30SRHh0wa7fWW18y3W5KnL3vzo0XUiUhj58KSimlVPlJz29vV9CES0CteQtKTeDEvYsdQlmTduU7mLmt0cq2UkqpNi14+v5IXy87bWjsUVQ9dDnhW8t4EHPHKsJ3XkD1+CuwuncsdjQ5Cd1wRrFDKFnW0NL9wqRyo91IlFJKtUk7Bp4J4Ru/DdujgJc/Xvp7k/tYe5XfpEzSpX3ZVLIBpFcn7F16A2B/Y7dGSrc9VqbJw1RZ0ZZtpZRSFSP0wxNzK9ildpYQqQrWG9BYNe4SQj86KV+hFVz4D+cAXj7wstDJuwb2kXsA3kRYoe8fXcyIyobsrHnQy4m2bCullKoY9gG5zagnXdtjDeuNO30R0jNzK7BUh/IZWmG1D2P17epNJV/gyX3yxR41FLEES2dBbDIdHFleyuMdqZRSSuUo9OsziP3u31m3S69OBM89BGu3Ptj7DcLqVd554q39BxEcfRAAEg4WOZrciQj2QWXSCl9iynmm17ZIK9tKKaUqij2sd9Ztof85ETutJVVKuKIduuRI4s9Ow/nP3AbLBU/bH6tft1aKSpWEMrl7oTzaZ1sppVSbYZdRlwXp1kH7MCtVAbSyrZRSSpWzPE7rrsqEtmyXFa1sK6WUUuWswmeaVPVJVfn0zVda2VZKKaWUKivStX2xQ1BNoJVtpZRSFSvwnQOLHUKLha4pn1zfqrDCfzyP0NXHYw3ZqdihqCbQTj9KKaUqnrVbH4KXHFnsMJrF3n9Qg9tlp06tE4gqmuAVx+LOWuqlqSzhDDoqM61sK6WUqnjWrr2xencpdhj5FbSpvv/SYkehWkHgkGFwyLBih6GaSbuRKKWUUmWo6u8XFzsEpVQOWlTZFpFuIjJJROb7P7tmKTfGLzNfRMakrb9VRJaKyNY65cMi8oSILBCRD0RkUEviVEoppSpNOc0WqVRb1tKW7euBycaYYcBk/3ktItINuBEYBRwE3JhWKX/RX1fXWGCDMWYX4C7g9hbGqZRSqg2xDxxC6McnFzuMgrF27VPsEJRSOWppZft0YLy/PB44I0OZE4FJxpj1xpgNwCTgJABjzPvGmBWNHPdp4FgR0bT9SimlchK6+gTsfXdGOrcDSP2sGB3CxY5AKZWjlla2eyUry/7PTLlo+gFL054v89c1JLWPMSYBbAK6tzBWpZRSbYz9jd0JXnkc9rEjih1Ki4T/dH7tFTqRjVJlo9FsJCLyBtA7w5IXqDAAAAXPSURBVKZf5XiOTC3SjX1M5LyPiFwGXOY/3Soic3OMK596AGuLcF6Vf3otK4tez8qh1zLdBODHxQ6i2fRaVo62fi13zqVQo5VtY8xx2baJyCoR6WOMWSEifYDVGYotA45Ke94fmNLIaZcBA4BlIhIAOgPrs8R3L3BvI8crKBGZbowZWcwYVH7otawsej0rh17LyqHXsnLotcxNS7uRvAAks4uMAZ7PUOY14AQR6eoPjDzBX5frcUcDbxpj9KaZUkoppZQqKy2tbN8GHC8i84Hj/eeIyEgRuR/AGLMeuAWY5j9u9tchIn8UkWVAOxFZJiI3+cd9AOguIguAa8mQ5UQppZRSSqlSJ9pg3HIicpnfnUWVOb2WlUWvZ+XQa1k59FpWDr2WudHKtlJKKaWUUgWi07UrpZRSSilVIFrZbiEROUlE5vpTy2vf8hIiIotF5DMR+UREpvvruonIJBGZ7//s6q8XEfmrfx0/FZH9044zxi8/X0TGpK0/wD/+An9fnXgpT0TkQRFZLSKz0tYV/NplO4dqvizX8iYR+dp/b34iIqekbfuFf13misiJaeszftaKyGAR+cC/Zk+ISMhfH/afL/C3D2qd37hyicgAEXlLROaIyGwRucZfr+/NMtPAtdT3ZiEYY/TRzAdgAwuBIUAImAkML3Zc+khdn8VAjzrr/ghc7y9fD9zuL58CvIKX4/1g4AN/fTfgS/9nV3+5q7/tQ+AQf59XgJOL/TtXygM4AtgfmNWa1y7bOfSR92t5E/DTDGWH+5+jYWCw//lqN/RZCzwJnOsvjwN+4C9fCYzzl88Fnij2a1HuD6APsL+/3BGY518zfW+W2aOBa6nvzQI8tGW7ZQ4CFhhjvjTGxIDH8aaaV6XrdGC8vzweOCNt/QTjeR/oIl7u+BOBScaY9caYDcAk4CR/WydjzHvG+8SYkHYs1ULGmHeon1u/Na5dtnOoZspyLbM5HXjcGBM1xiwCFuB9zmb8rPVbPY8Bnvb3r/t3kbyWTwPH6t2nljHGrDDGfOQvbwHm4M34rO/NMtPAtcxG35stoJXtlmnOVPSq9RjgdRGZId5MowC9jDErwPuwAXby12e7lg2tX5ZhvSqc1rh22c6h8u9qv2vBg2ldApp6LbsDG40xiTrrax3L377JL6/ywL/1vx/wAfreLGt1riXoezPvtLLdMs2Zil61nsOMMfsDJwNXicgRDZTNdi2bul61Pr125ef/gKHAvsAK4H/99fm8lnqdC0REOgDPAD8yxmxuqGiGdfreLCEZrqW+NwtAK9stk5xWPqk/sLxIsag6jDHL/Z+rgefwbnet8m9V4v9c7RfPdi0bWt8/w3pVOK1x7bKdQ+WRMWaVMcYxxrjAfXjvTWj6tVyL1zUhUGd9rWP52zuTe3cWlYWIBPEqZ48aY571V+t7swxlupb63iwMrWy3zDRgmD/iNoTX0f+FIsekABFpLyIdk8vACcAsvOuTHPk+BnjeX34BuMgfPX8wsMm/VfkacIKIdPVvp50AvOZv2yIiB/t9zS5KO5YqjNa4dtnOofIoWWnynYn33gTv9T/Xz1YwGBiGN2Au42et36/3LWC0v3/dv4vktRwNvOmXV83kv18eAOYYY+5M26TvzTKT7Vrqe7NAij1Cs9wfeKOt5+GNxv1VsePRR+q6DMEbFT0TmJ28Nnj9wiYD8/2f3fz1Avzdv46fASPTjnUJ3mCQBcD30taPxPsgWgj8DX+SKH3k5fr9C+8WZhyvFWRsa1y7bOfQR96v5cP+tfoU7x9vn7Tyv/Kvy1zSMvxk+6z13+sf+tf4KSDsr6/yny/wtw8p9mtR7g/gcLzb/Z8Cn/iPU/S9WX6PBq6lvjcL8NAZJJVSSimllCoQ7UailFJKKaVUgWhlWymllFJKqQLRyrZSSimllFIFopVtpZRSSimlCkQr20oppZRSShWIVraVUkoppZQqEK1sK6WUUkopVSBa2VZKKaWUUqpA/h9uOhvEyvJImQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f54325d94e0>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Plot Independent Component #1\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Independent Component #1')\n",
+    "plt.plot(result_signal_1, c=\"#df8efd\")\n",
+    "plt.ylim(-0.010, 0.010)\n",
+    "plt.show()\n",
+    "\n",
+    "# Plot Independent Component #2\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Independent Component #2')\n",
+    "plt.plot(result_signal_2, c=\"#87de72\")\n",
+    "plt.ylim(-0.010, 0.010)\n",
+    "plt.show()\n",
+    "\n",
+    "# Plot Independent Component #3\n",
+    "plt.figure(figsize=(12,2))\n",
+    "plt.title('Independent Component #3')\n",
+    "plt.plot(result_signal_3, c=\"#f65e97\")\n",
+    "plt.ylim(-0.010, 0.010)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Do some of these look like musical wave forms? \n",
+    "\n",
+    "The best way to confirm the result is to listen to resulting files. So let's save as wave files and verify. But before we do that, we'll have to:\n",
+    "* convert them to integer (so we can save as PCM 16-bit Wave files), otherwise only some media players would be able to play them and others won't\n",
+    "* Map the values to the appropriate range for int16 audio. That range is between -32768 and +32767. A basic mapping can be done by multiplying by 32767.\n",
+    "* The sounds will be a little faint, we can increase the volume by multiplying by a value like 100"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.io import wavfile\n",
+    "\n",
+    "# Convert to int, map the appropriate range, and increase the volume a little bit\n",
+    "result_signal_1_int = np.int16(result_signal_1*32767*100)\n",
+    "result_signal_2_int = np.int16(result_signal_2*32767*100)\n",
+    "result_signal_3_int = np.int16(result_signal_3*32767*100)\n",
+    "\n",
+    "\n",
+    "# Write wave files\n",
+    "wavfile.write(\"result_signal_1.wav\", fs, result_signal_1_int)\n",
+    "wavfile.write(\"result_signal_2.wav\", fs, result_signal_2_int)\n",
+    "wavfile.write(\"result_signal_3.wav\", fs, result_signal_3_int)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The resulting files we have now are: [note: make sure to lower the volume on your speakers first, just in case some problem caused the file to sound like static]\n",
+    "* [result_signal_1.wav](result_signal_1.wav)\n",
+    "* [result_signal_2.wav](result_signal_2.wav)\n",
+    "* [result_signal_3.wav](result_signal_3.wav)\n",
+    "\n",
+    "\n",
+    "\n",
+    "Music:\n",
+    "* Piano - The Carnival of the Animals - XIII. The Swan (Solo piano version). Performer: Markus Staab\n",
+    "* Cello - Cello Suite no. 3 in C, BWV 1009 - I. Prelude. Performer: European Archive"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/python/Unsupervised Learning/Random Projection and ICA/ica.py b/python/Unsupervised Learning/Random Projection and ICA/ica.py
new file mode 100644
index 0000000..b7eee24
--- /dev/null
+++ b/python/Unsupervised Learning/Random Projection and ICA/ica.py	
@@ -0,0 +1,110 @@
+import numpy as np
+import wave
+import warnings
+import matplotlib.pyplot as plt
+from sklearn.decomposition import FastICA
+from scipy.io import wavfile
+
+
+warnings.filterwarnings("ignore")
+
+# Read the wave file
+mix_1_wave = wave.open('ICA mix 1.wav', 'r')
+
+mix_1_wave.getparams()
+
+length = 264515 / 44100
+
+# Extract Raw Audio from Wav File
+signal_1_raw = mix_1_wave.readframes(-1)
+signal_1 = np.fromstring(signal_1_raw, 'Int16')
+
+print('length: ', len(signal_1), 'first 100 elements: ', signal_1[:100])
+
+fs = mix_1_wave.getframerate()
+timing = np.linspace(0, len(signal_1) / fs, num=len(signal_1))
+
+
+plt.figure(figsize=(12, 2))
+plt.title('Recording 1')
+plt.plot(timing, signal_1, c="#3ABFE7")
+plt.ylim(-35000, 35000)
+plt.show()
+
+
+mix_2_wave = wave.open('ICA mix 2.wav', 'r')
+
+# Extract Raw Audio from Wav File
+signal_raw_2 = mix_2_wave.readframes(-1)
+signal_2 = np.fromstring(signal_raw_2, 'Int16')
+
+
+mix_3_wave = wave.open('ICA mix 3.wav', 'r')
+
+# Extract Raw Audio from Wav File
+signal_raw_3 = mix_3_wave.readframes(-1)
+signal_3 = np.fromstring(signal_raw_3, 'Int16')
+
+
+plt.figure(figsize=(12, 2))
+plt.title('Recording 2')
+plt.plot(timing, signal_2, c="#3ABFE7")
+plt.ylim(-35000, 35000)
+plt.show()
+
+
+plt.figure(figsize=(12, 2))
+plt.title('Recording 3')
+plt.plot(timing, signal_3, c="#3ABFE7")
+plt.ylim(-35000, 35000)
+plt.show()
+
+X = list(zip(signal_1, signal_2, signal_3))
+
+# Let's peak at what X looks like
+print(X[:10])
+
+# TODO: Initialize FastICA with n_components=3
+ica = FastICA(n_components=3)
+
+# TODO: Run the FastICA algorithm using fit_transform on dataset X
+ica_result = ica.fit_transform(X)
+
+print(ica_result.shape)
+
+result_signal_1 = ica_result[:, 0]
+result_signal_2 = ica_result[:, 1]
+result_signal_3 = ica_result[:, 2]
+
+# Plot Independent Component #1
+plt.figure(figsize=(12, 2))
+plt.title('Independent Component #1')
+plt.plot(result_signal_1, c="#df8efd")
+plt.ylim(-0.010, 0.010)
+plt.show()
+
+# Plot Independent Component #2
+plt.figure(figsize=(12, 2))
+plt.title('Independent Component #2')
+plt.plot(result_signal_2, c="#87de72")
+plt.ylim(-0.010, 0.010)
+plt.show()
+
+# Plot Independent Component #3
+plt.figure(figsize=(12, 2))
+plt.title('Independent Component #3')
+plt.plot(result_signal_3, c="#f65e97")
+plt.ylim(-0.010, 0.010)
+plt.show()
+
+
+# Convert to int, map the appropriate range, and increase the volume
+result_signal_1_int = np.int16(result_signal_1 * 32767 * 100)
+result_signal_2_int = np.int16(result_signal_2 * 32767 * 100)
+result_signal_3_int = np.int16(result_signal_3 * 32767 * 100)
+
+
+# Write wave files
+wavfile.write("result_signal_1.wav", fs, result_signal_1_int)
+wavfile.write("result_signal_2.wav", fs, result_signal_2_int)
+wavfile.write("result_signal_3.wav", fs, result_signal_3_int)
diff --git a/python/Unsupervised Learning/Random Projection and ICA/result_signal_1.wav b/python/Unsupervised Learning/Random Projection and ICA/result_signal_1.wav
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diff --git a/python/Unsupervised Learning/Random Projection and ICA/result_signal_3.wav b/python/Unsupervised Learning/Random Projection and ICA/result_signal_3.wav
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