Principle_Component_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Principle Component Analysis from Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### This notebook walks through the idea behind principle component analysis and shows step by step process behind the scenes.\n",
    "##### It also shows the implementation with Scikit-learn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### This tutoal is based on:  https://sebastianraschka.com/Articles/2015_pca_in_3_steps.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\n",
    "    filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',\n",
    "    header=None,\n",
    "    sep=',')\n",
    "\n",
    "df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']\n",
    "df.dropna(how=\"all\", inplace=True) # drops the empty line at file-end"
   ]
  },
  {
   "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>sepal_len</th>\n",
       "      <th>sepal_wid</th>\n",
       "      <th>petal_len</th>\n",
       "      <th>petal_wid</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>146</td>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>147</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>148</td>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_len  sepal_wid  petal_len  petal_wid           class\n",
       "145        6.7        3.0        5.2        2.3  Iris-virginica\n",
       "146        6.3        2.5        5.0        1.9  Iris-virginica\n",
       "147        6.5        3.0        5.2        2.0  Iris-virginica\n",
       "148        6.2        3.4        5.4        2.3  Iris-virginica\n",
       "149        5.9        3.0        5.1        1.8  Iris-virginica"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define X and y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up X and y as matrices\n",
    "X = df.iloc[:,:4].values\n",
    "y = df.iloc[:, -1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'], dtype=object)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['class'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class'], dtype='object')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "label_dict = {1: 'Iris-Setosa',\n",
    "              2: 'Iris-Versicolor',\n",
    "              3: 'Iris-Virgnica'}\n",
    "\n",
    "feature_dict = {0: 'sepal length [cm]',\n",
    "                1: 'sepal width [cm]',\n",
    "                2: 'petal length [cm]',\n",
    "                3: 'petal width [cm]'}\n",
    "\n",
    "with plt.style.context('seaborn-whitegrid'):\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    for cnt in range(4):\n",
    "        plt.subplot(2, 2, cnt+1)\n",
    "        for lab in ('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'):\n",
    "            plt.hist(X[y==lab, cnt],\n",
    "                     label=lab,\n",
    "                     bins=10,\n",
    "                     alpha=0.3,)\n",
    "        plt.xlabel(feature_dict[cnt])\n",
    "    plt.legend(loc='upper right', fancybox=True, fontsize=8)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Standardize the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_std = StandardScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculate the covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate mean for each COLUMN in X\n",
    "mean_vec = np.mean(X_std, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the covariance of X (feature matrix)\n",
    "m = len(X) # No.instances \n",
    "cov_mat = 1/(m-1) * (X_std - mean_vec).T.dot(X_std - mean_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix \n",
      "[[ 1.00671141 -0.11010327  0.87760486  0.82344326]\n",
      " [-0.11010327  1.00671141 -0.42333835 -0.358937  ]\n",
      " [ 0.87760486 -0.42333835  1.00671141  0.96921855]\n",
      " [ 0.82344326 -0.358937    0.96921855  1.00671141]]\n"
     ]
    }
   ],
   "source": [
    "print('Covariance matrix \\n%s' %cov_mat)\n",
    "# Covariance matrix is (n x n) , n: features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPy covariance matrix: \n",
      "[[ 1.00671141 -0.11010327  0.87760486  0.82344326]\n",
      " [-0.11010327  1.00671141 -0.42333835 -0.358937  ]\n",
      " [ 0.87760486 -0.42333835  1.00671141  0.96921855]\n",
      " [ 0.82344326 -0.358937    0.96921855  1.00671141]]\n"
     ]
    }
   ],
   "source": [
    "# We could also use np.cov to calculate covariance matrix directly\n",
    "\n",
    "print('NumPy covariance matrix: \\n%s' %np.cov(X_std.T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Apply eigendecomposition on covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvectors \n",
      "[[ 0.52237162 -0.37231836 -0.72101681  0.26199559]\n",
      " [-0.26335492 -0.92555649  0.24203288 -0.12413481]\n",
      " [ 0.58125401 -0.02109478  0.14089226 -0.80115427]\n",
      " [ 0.56561105 -0.06541577  0.6338014   0.52354627]]\n",
      "\n",
      "Eigenvalues \n",
      "[2.93035378 0.92740362 0.14834223 0.02074601]\n"
     ]
    }
   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(cov_mat)\n",
    "\n",
    "print('Eigenvectors \\n%s' %eig_vecs)\n",
    "print('\\nEigenvalues \\n%s' %eig_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvectors \n",
      "[[ 0.52237162 -0.37231836 -0.72101681  0.26199559]\n",
      " [-0.26335492 -0.92555649  0.24203288 -0.12413481]\n",
      " [ 0.58125401 -0.02109478  0.14089226 -0.80115427]\n",
      " [ 0.56561105 -0.06541577  0.6338014   0.52354627]]\n",
      "\n",
      "Eigenvalues \n",
      "[2.91081808 0.92122093 0.14735328 0.02060771]\n"
     ]
    }
   ],
   "source": [
    "# Eigenvalue decomposition based on correlation matrix\n",
    "# Same results as above\n",
    "\n",
    "cor_mat1 = np.corrcoef(X_std.T)\n",
    "\n",
    "eig_vals, eig_vecs = np.linalg.eig(cor_mat1)\n",
    "\n",
    "print('Eigenvectors \\n%s' %eig_vecs)\n",
    "print('\\nEigenvalues \\n%s' %eig_vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### While the eigendecomposition of the covariance or correlation matrix may be more intuitiuve, most PCA implementations perform a Singular Value Decomposition (SVD) to improve the computational efficiency. So, let us perform an SVD to confirm that the result are indeed the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "u,s,v = np.linalg.svd(X_std.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.52237162, -0.37231836,  0.72101681,  0.26199559],\n",
       "       [ 0.26335492, -0.92555649, -0.24203288, -0.12413481],\n",
       "       [-0.58125401, -0.02109478, -0.14089226, -0.80115427],\n",
       "       [-0.56561105, -0.06541577, -0.6338014 ,  0.52354627]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20.89551896, 11.75513248,  4.7013819 ,  1.75816839])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sorting eigenpairs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The typical goal of a PCA is to reduce the dimensionality of the original feature space by projecting it onto a smaller subspace, where the eigenvectors will form the axes. However, the eigenvectors only define the directions of the new axis, since they have all the same unit length 1, which can confirmed by the following two lines of code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "1.0\n",
      "1.0\n",
      "0.9999999999999998\n"
     ]
    }
   ],
   "source": [
    "for i in eig_vecs:\n",
    "    print(np.linalg.norm(i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rank the eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a set with eigenvalues and eigenvectors\n",
    "\n",
    "eig_pairs = [(np.abs(eig_vals[i]), np.abs(eig_vecs[:, i])) for i in range(len(eig_vals))]\n",
    "eig_pairs.sort(key = lambda x: x[0], reverse = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.52237162 -0.26335492  0.58125401  0.56561105]\n",
      "[-0.37231836 -0.92555649 -0.02109478 -0.06541577]\n",
      "[-0.72101681  0.24203288  0.14089226  0.6338014 ]\n",
      "[ 0.26199559 -0.12413481 -0.80115427  0.52354627]\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(eig_vecs)):\n",
    "    print(eig_vecs[:,i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9108180837520536\n",
      "0.9212209307072253\n",
      "0.14735327830509562\n",
      "0.02060770723562562\n"
     ]
    }
   ],
   "source": [
    "# Confirm that eigenvalues are sorted in descending order\n",
    "for i, j in eig_pairs:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explained variance\n",
    "After sorting the eigenpairs, the next question is “how many principal components are we going to choose for our new feature subspace?” A useful measure is the so-called “explained variance,” which can be calculated from the eigenvalues. The explained variance tells us how much information (variance) can be attributed to each of the principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "total = sum(eig_vals)\n",
    "variance_explained = [i/total for i in sorted(eig_vals, reverse = True)]\n",
    "cumulative_variance_explain = np.cumsum(variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.7277045209380134,\n",
       " 0.23030523267680633,\n",
       " 0.036838319576273905,\n",
       " 0.005151926808906405]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variance_explained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "tot = sum(eig_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize= (12,6))\n",
    "\n",
    "plt.bar(range(4), var_exp, alpha = 0.5, align = 'center', label = 'individual variance xplained')\n",
    "plt.step(range(4), cum_var_exp, label = 'cumulative variance explained')\n",
    "\n",
    "plt.xlabel(\"No. PC\")\n",
    "plt.ylabel(\"Explained variance\")\n",
    "plt.legend(loc = 'best')\n",
    "#plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The plot above clearly shows that most of the variance (72.77% of the variance to be precise) can be explained by the first principal component alone. The second principal component still bears some information (23.03%) while the third and fourth principal components can safely be dropped without losing to much information. Together, the first two principal components contain 95.8% of the information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Projection matrix\n",
    "Matrix of the top k eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[0.52237162 0.37231836]\n",
      " [0.26335492 0.92555649]\n",
      " [0.58125401 0.02109478]\n",
      " [0.56561105 0.06541577]]\n"
     ]
    }
   ],
   "source": [
    "W = np.hstack((eig_pairs[0][1].reshape(4,1),\n",
    "             eig_pairs[1][1].reshape(4,1)))\n",
    "\n",
    "print(\"Matrix W:\\n\", W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Project X onto the new feature space\n",
    "In this last step we will use the 4×2-dimensional projection matrix W to transform our samples onto the new subspace via the equation\n",
    "Y=X×W, where Y is a 150×2 matrix of our transformed samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_proj = X.dot(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12, 8))\n",
    "for label, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),\n",
    "                        ('blue', 'red', 'green')):\n",
    "    plt.scatter(X_proj[y==label,0],\n",
    "               X_proj[y==label, 1],\n",
    "               label= label,\n",
    "               c = col)\n",
    "    \n",
    "plt.xlabel(\"principle component 1\", fontsize = 12)\n",
    "plt.ylabel('principle component 2', fontsize = 12)\n",
    "plt.legend(loc = 'upper right')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PCA in Scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 2)\n",
    "X2D = pca.fit_transform(X_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "for label, color in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),\n",
    "                        ('blue', 'red', 'green')):\n",
    "    plt.scatter(X2D[y==label, 0],\n",
    "               X2D[y==label, 1],\n",
    "               label = label, \n",
    "               color = color)\n",
    "    \n",
    "    \n",
    "plt.xlabel('principle component 1')\n",
    "plt.ylabel('principle component 2')\n",
    "plt.legend(loc = 'upper right')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}