module 3/Principle Component Analysis (PCA) for Data Visualization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <img style=\"float: left; padding-right: 100px; width: 300px\" src=\"../images/logo.png\">AI4SG Bootcamp:\n",
    "\n",
    "\n",
    "##  PCA  for Data Visualization\n",
    "**Authors:** Davis David\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length  sepal width  petal length  petal width       target\n",
       "0           5.1          3.5           1.4          0.2  Iris-setosa\n",
       "1           4.9          3.0           1.4          0.2  Iris-setosa\n",
       "2           4.7          3.2           1.3          0.2  Iris-setosa\n",
       "3           4.6          3.1           1.5          0.2  Iris-setosa\n",
       "4           5.0          3.6           1.4          0.2  Iris-setosa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n",
    "# loading dataset into Pandas DataFrame\n",
    "df = pd.read_csv(url, names=['sepal length','sepal width','petal length','petal width','target'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardize the Data\n",
    "\n",
    "Since PCA yields a feature subspace that maximizes the variance along the axes, it makes sense to standardize the data, especially, if it was measured on different scales. Although, all features in the Iris dataset were measured in centimeters, let us continue with the transformation of the data onto unit scale (mean=0 and variance=1), which is a requirement for the optimal performance of many machine learning algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "features = ['sepal length', 'sepal width', 'petal length', 'petal width']\n",
    "x = df.loc[:, features].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df.loc[:,['target']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = StandardScaler().fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.900681</td>\n",
       "      <td>1.032057</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.143017</td>\n",
       "      <td>-0.124958</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.385353</td>\n",
       "      <td>0.337848</td>\n",
       "      <td>-1.398138</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.506521</td>\n",
       "      <td>0.106445</td>\n",
       "      <td>-1.284407</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.021849</td>\n",
       "      <td>1.263460</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length  sepal width  petal length  petal width\n",
       "0     -0.900681     1.032057     -1.341272    -1.312977\n",
       "1     -1.143017    -0.124958     -1.341272    -1.312977\n",
       "2     -1.385353     0.337848     -1.398138    -1.312977\n",
       "3     -1.506521     0.106445     -1.284407    -1.312977\n",
       "4     -1.021849     1.263460     -1.341272    -1.312977"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data = x, columns = features).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA Projection to 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "principalComponents = pca.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a dataframe for principal components \n",
    "principalDf = pd.DataFrame(data = principalComponents\n",
    "             , columns = ['principal component 1', 'principal component 2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>principal component 1</th>\n",
       "      <th>principal component 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.264542</td>\n",
       "      <td>0.505704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.086426</td>\n",
       "      <td>-0.655405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.367950</td>\n",
       "      <td>-0.318477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.304197</td>\n",
       "      <td>-0.575368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.388777</td>\n",
       "      <td>0.674767</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   principal component 1  principal component 2\n",
       "0              -2.264542               0.505704\n",
       "1              -2.086426              -0.655405\n",
       "2              -2.367950              -0.318477\n",
       "3              -2.304197              -0.575368\n",
       "4              -2.388777               0.674767"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the first five values\n",
    "principalDf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        target\n",
       "0  Iris-setosa\n",
       "1  Iris-setosa\n",
       "2  Iris-setosa\n",
       "3  Iris-setosa\n",
       "4  Iris-setosa"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the target class values \n",
    "df[['target']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>principal component 1</th>\n",
       "      <th>principal component 2</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.264542</td>\n",
       "      <td>0.505704</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.086426</td>\n",
       "      <td>-0.655405</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.367950</td>\n",
       "      <td>-0.318477</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.304197</td>\n",
       "      <td>-0.575368</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.388777</td>\n",
       "      <td>0.674767</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   principal component 1  principal component 2       target\n",
       "0              -2.264542               0.505704  Iris-setosa\n",
       "1              -2.086426              -0.655405  Iris-setosa\n",
       "2              -2.367950              -0.318477  Iris-setosa\n",
       "3              -2.304197              -0.575368  Iris-setosa\n",
       "4              -2.388777               0.674767  Iris-setosa"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "finalDf = pd.concat([principalDf, df[['target']]], axis = 1)\n",
    "finalDf.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize 2D Projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (15,10))\n",
    "ax = fig.add_subplot(1,1,1) \n",
    "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
    "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
    "ax.set_title('2 Component PCA', fontsize = 20)\n",
    "\n",
    "\n",
    "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n",
    "colors = ['r', 'g', 'b']\n",
    "for target, color in zip(targets,colors):\n",
    "    indicesToKeep = finalDf['target'] == target\n",
    "    ax.scatter(finalDf.loc[indicesToKeep, 'principal component 1']\n",
    "               , finalDf.loc[indicesToKeep, 'principal component 2']\n",
    "               , c = color\n",
    "               , s = 50)\n",
    "ax.legend(targets)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The three classes appear to be well separated!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explained Variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The explained variance tells us how much information (variance) can be attributed to each of the principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.72770452, 0.23030523])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Together, the first two principal components contain 95.80% of the information. The first principal component contains 72.77% of the variance and the second principal component contains 23.03% of the variance. The third and fourth principal component contained the rest of the variance of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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