{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <p style=\"text-align: right;\"> &#9989; Put your name here</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Day 12 Pre-Class Assignment: Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goals for today's pre-class assignment \n",
    "\n",
    "1. Review of Python Modules\n",
    "2. Matrices and their eigenvalues/eigenvectors\n",
    "3. Example Application: The Iris data set\n",
    "\n",
    "## Assignment instructions\n",
    "\n",
    "**This assignment is due by 11:59 p.m. the day before class** and should be uploaded into the appropriate \"Pre-class assignments\" submission folder in the Desire2Learn website. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "# 1. Review of Python Modules\n",
    "Run the following cell to load the modules we will be using in this pre-class assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import scipy.linalg\n",
    "import sklearn.decomposition as dec\n",
    "import sklearn.datasets as ds\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question**: Identify the 5 modules we've imported, and their function. (the first one is done for you and the last one should be pretty familiar to you)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <font size=8 color=\"#009600\">&#9998;</font> Do This - Erase this first line of this cell and finish describing the remaining four modules. Use appropriate markdown to make your answer readable. (double-click on this text to edit this cell, and hit shift+enter to save the text)\n",
    " \n",
    "1. **numpy** (imported as np): A platform for numerical and scientific computing in Python. It provides multi-dimensional arrays (e.g., those from linear algebra) and tools for working with them.\n",
    "2. ...\n",
    "3. ...\n",
    "4. ...\n",
    "5. ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# 2. Intuition about principal component analysis\n",
    "\n",
    "The following videos (Developed at Georgia Tech) are to help you gain an understanding and intuition about principal component analysis (PCA). PCA is one of the main techniques used in data science, exploratory data analysis and modeling.\n",
    "\n",
    "You can watch the entire course here:\n",
    "\n",
    "https://youtu.be/Ki2iHgKxRBo?list=PLAwxTw4SYaPl0N6-e1GvyLp5-MUMUjOKo\n",
    "\n",
    "It's really good but we don't have time to cover it all. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/kw9R0nD69OU\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x20f8c9fbe88>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"kw9R0nD69OU\",width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question**: PCA is trying to find the directions with maximal what? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=8 color=\"#009600\">&#9998;</font> Do This - Erase the contents of this cell and replace it with your answer to the above question!  (double-click on this text to edit this cell, and hit shift+enter to save the text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/_nZUhV-qhZA\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x20f8ca18908>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"_nZUhV-qhZA\",width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question**: This video introduces a concept of \"features\" in a dataset. What are the names of the two original features represented in the graph shown in this video. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=8 color=\"#009600\">&#9998;</font> Do This - Erase the contents of this cell and replace it with your answer to the above question!  (double-click on this text to edit this cell, and hit shift+enter to save the text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/kuzJJgPBrqc\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x20f8ca22908>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"kuzJJgPBrqc\",width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question**: What does it mean if eigenvalue of a dimension is zero? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=8 color=\"#009600\">&#9998;</font> Do This - Erase the contents of this cell and replace it with your answer to the above question!  (double-click on this text to edit this cell, and hit shift+enter to save the text)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# 3. Example Application: The Iris data set\n",
    "\n",
    "Let's go back to the Iris data set, but this time let's just load it using `sklearn`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 4)\n"
     ]
    }
   ],
   "source": [
    "# Let us first load the data set\n",
    "\n",
    "iris = ds.load_iris()\n",
    "data = iris.data\n",
    "target = iris.target\n",
    "print(data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember about the Iris data set. The three classes in the Iris dataset are represented by numbers in the 'target' vector:\n",
    "\n",
    "    1. Iris-setosa (n=50)\n",
    "    2. Iris-versicolor (n=50)\n",
    "    3. Iris-virginica (n=50)\n",
    "\n",
    "There are four measurements (features) for each flower in the  'data' matrix:    \n",
    "    1. sepal length in cm\n",
    "    2. sepal width in cm\n",
    "    3. petal length in cm\n",
    "    4. petal width in cm\n",
    "    \n",
    "Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://nbviewer.jupyter.org/github/rasbt/pattern_classification/blob/master/Images/iris_petal_sepal.png\" alt=\"Image of flower\" width=400px>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Our Goal:** Create a model that given the four measurements can predicts the iris class.  We will use PCA to find axes that make it easer to separate the data into classes.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step A: Try to visualize the features by plotting them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#9989; **Question**: Modify the following code to draw a scatterplot of the data for just the first and second axes of the data matrix (index 0 and 1).  Hint: use a similar vector notation as step C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x216 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# DO THIS: Modify the code below to do a scatter plot with respect to the first two variables of the data\n",
    "# i.e. all rows but just the first and second columns.\n",
    "plt.figure(figsize=(6,3));\n",
    "#plt.scatter(  ,   , c=target, s=30, cmap=plt.cm.rainbow);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If done correctly the above should show different color dots for each of the different iris types.  As you can see, the classes do not separate clearly. Perhaps there are two directions that separate the data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step B: Transform the data in terms of its principal components\n",
    "Now we will use a PCA algorithm. Fortunately there is a simple PCA function available in the sklearn module. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = dec.PCA()\n",
    "pca_data = pca.fit_transform(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Out of curiosity. print the eigenvalues.  Remember from the video that low eigenvalues indicate less information. Big eigenvalues indicate more information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.22824171 0.24267075 0.0782095  0.02383509]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step C: Now plot the transformed data in terms of its first two principal components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,3));\n",
    "plt.scatter(pca_data[:,0], pca_data[:,1], c=target, s=30, cmap=plt.cm.rainbow);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:**  Describe in words the differences between the graphs from Step A and Step C.  They are representing the same data.  Why would we prefer to use the features in step C?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=8 color=\"#009600\">&#9998;</font> Do This - Erase the contents of this cell and replace it with your answer to the above question!  (double-click on this text to edit this cell, and hit shift+enter to save the text)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "# Assignment wrap-up\n",
    "\n",
    "Please fill out the form that appears when you run the code below.  **You must completely fill this out in order to receive credit for the assignment!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import HTML\n",
    "HTML(\n",
    "\"\"\"\n",
    "<iframe \n",
    "\tsrc=\"https://cmse.msu.edu/cmse202-pc-survey\" \n",
    "\twidth=\"800px\" \n",
    "\theight=\"600px\" \n",
    "\tframeborder=\"0\" \n",
    "\tmarginheight=\"0\" \n",
    "\tmarginwidth=\"0\">\n",
    "\tLoading...\n",
    "</iframe>\n",
    "\"\"\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "### Congratulations, you're done with your pre-class assignment!\n",
    "\n",
    "Now, you just need to submit this assignment by uploading it to the course <a href=\"https://d2l.msu.edu/\">Desire2Learn</a> web page for today's submission folder (Don't forget to add your name in the first cell)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#169; Copyright Michigan State University Board of Trustees"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}