PCA-2-features.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e8abb3c3",
   "metadata": {},
   "source": [
    "# Principal Component Analysys (PCA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "307fcb72",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "40e0c3b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating data\n",
    "x = np.array([1.1, 1.3, 1.6, 1.4, 2.4, 2.8, 3.1, 3.4, 3.8, 4, 3.6, 4.1, 3.9, 4.6]) # x data\n",
    "y = np.array([20.1, 30, 30.6, 30.2, 40.0, 40.5, 41, 43.4, 46.2, 48, 50.3, 60, 62, 64.2]) # y data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "80c2da91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting data\n",
    "plt.figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "plt.scatter(x,y, label=\"data points\",zorder=2, s=40) # points\n",
    "plt.scatter(x.mean(), y.mean(), c=\"r\", s=200, label=\"mean\", zorder=2)\n",
    "\n",
    "plt.grid(1, zorder=1)\n",
    "plt.legend()\n",
    "plt.title(\"data\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "496b33de",
   "metadata": {},
   "source": [
    "# Feature Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d0c4bd28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.05714286, 0.14285714, 0.08571429, 0.37142857,\n",
       "       0.48571429, 0.57142857, 0.65714286, 0.77142857, 0.82857143,\n",
       "       0.71428571, 0.85714286, 0.8       , 1.        ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = x_ = (x - x.min()) / (x.max() - x.min())\n",
    "y = y_ = (y - y.min()) / (y.max() - y.min())\n",
    "\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "320a1d3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting data\n",
    "plt.figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "plt.scatter(x,y, label=\"data points\", zorder=3) # points\n",
    "plt.plot([-0.1,1.1],np.zeros(2), \"k\", zorder=1) # line x = 0\n",
    "plt.plot(np.zeros(2),[-0.1,1.1], \"k\", zorder=1) # line y = 0\n",
    "plt.scatter(x.mean(), y.mean(), c=\"r\", s=200, label=\"mean\", zorder=2)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.xlim([-0.1,1.1])\n",
    "plt.ylim([-0.1,1.1])\n",
    "plt.title(\"scaled\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67a9cfeb",
   "metadata": {},
   "source": [
    "# Mean Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7a8ad2c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.5244898 , -0.46734694, -0.38163265, -0.43877551, -0.15306122,\n",
       "       -0.03877551,  0.04693878,  0.13265306,  0.24693878,  0.30408163,\n",
       "        0.18979592,  0.33265306,  0.2755102 ,  0.4755102 ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x -= x.mean() # subtracting mean\n",
    "y -= y.mean()\n",
    "\n",
    "x "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a04303ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "now means of our features are equal to 0\n",
      "x.mean().round() = 0.0\n",
      "y.mean().round() = -0.0\n"
     ]
    }
   ],
   "source": [
    "print(f\"now means of our features are equal to 0\\n{x.mean().round() = }\\n{y.mean().round() = }\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5a396bae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting data\n",
    "plt.figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "plt.scatter(x,y, label=\"data points\", zorder=2) # points\n",
    "plt.plot([-0.6,0.6],np.zeros(2), \"k\", zorder=1) # line x = 0\n",
    "plt.plot(np.zeros(2),[-0.6,0.6], \"k\", zorder=1) # line y = 0\n",
    "plt.scatter(x.mean(), y.mean(), c=\"r\", s=200, label=\"mean\", zorder=3)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.xlim([-0.6,0.6])\n",
    "plt.ylim([-0.6,0.6])\n",
    "plt.title(\"scaled and normalized data\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3c8a8b5",
   "metadata": {},
   "source": [
    "# Calculating Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5a7b92fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5244898 ,  0.46734694,  0.38163265,  0.43877551,  0.15306122,\n",
       "         0.03877551, -0.04693878, -0.13265306, -0.24693878, -0.30408163,\n",
       "        -0.18979592, -0.33265306, -0.2755102 , -0.4755102 ],\n",
       "       [ 0.52656301,  0.30207321,  0.28846777,  0.29753806,  0.07531584,\n",
       "         0.06397797,  0.0526401 , -0.00178167, -0.06527373, -0.10609006,\n",
       "        -0.15824425, -0.3781989 , -0.42355037, -0.47343699]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating matrix out of my feature vectors\n",
    "X = np.vstack([-x, -y]) # \"-\" fix\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b9a62cff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating covariance matrix \n",
    "X_cov = np.cov(X) # or X @ X.T\n",
    "X_cov.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b54723e3",
   "metadata": {},
   "source": [
    "# Calculating Eigectors and Eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c70f6f6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.75429583, -0.65653469],\n",
       "       [ 0.65653469,  0.75429583]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eig_val, eig_vec = np.linalg.eig(X_cov) # can also use np.linalg.svd(X_cov)\n",
    "eig_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8b9b8803",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.75429583, 0.65653469])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eig_vec_1d = eig_vec[:,0]\n",
    "eig_vec_1d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b10a8695",
   "metadata": {},
   "source": [
    "# Transforming Original Data into 1 dim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3cc97442",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.74132735],\n",
       "       [ 0.55083939],\n",
       "       [ 0.47725302],\n",
       "       [ 0.5263106 ],\n",
       "       [ 0.16490091],\n",
       "       [ 0.07125196],\n",
       "       [-0.00084567],\n",
       "       [-0.10122938],\n",
       "       [-0.22911936],\n",
       "       [-0.29901931],\n",
       "       [-0.24705511],\n",
       "       [-0.49921951],\n",
       "       [-0.48589171],\n",
       "       [-0.66950317]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data1 = np.dot(eig_vec_1d, X).reshape(-1, 1)\n",
    "new_data1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "72a0f3d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,4))\n",
    "plt.plot(new_data1, np.zeros_like(new_data1), 'o', c=\"c\", label=\"datapoints\") # ploting the data\n",
    "plt.grid()\n",
    "plt.title(\"data in 1 dimension\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49cd3e93",
   "metadata": {},
   "source": [
    "# Testing Results Using PCA From Sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "926fff32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.74132735],\n",
       "       [ 0.55083939],\n",
       "       [ 0.47725302],\n",
       "       [ 0.5263106 ],\n",
       "       [ 0.16490091],\n",
       "       [ 0.07125196],\n",
       "       [-0.00084567],\n",
       "       [-0.10122938],\n",
       "       [-0.22911936],\n",
       "       [-0.29901931],\n",
       "       [-0.24705511],\n",
       "       [-0.49921951],\n",
       "       [-0.48589171],\n",
       "       [-0.66950317]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = np.vstack([x_, y_]).T # creating matrix out of my feature vectors\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=1)\n",
    "pca.fit(Y)\n",
    "new_data2 = pca.transform(Y)\n",
    "\n",
    "new_data2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c1507697",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,4))\n",
    "plt.plot(new_data2, np.zeros_like(new_data2), 'o', c=\"c\", label=\"datapoints\") # ploting the data\n",
    "plt.grid()\n",
    "plt.title(\"data in 1 dimension\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d06ad73e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is equal: \n",
      "[ True] [0.741327] [0.741327]\n",
      "[ True] [0.550839] [0.550839]\n",
      "[ True] [0.477253] [0.477253]\n",
      "[ True] [0.526311] [0.526311]\n",
      "[ True] [0.164901] [0.164901]\n",
      "[ True] [0.071252] [0.071252]\n",
      "[ True] [-0.000846] [-0.000846]\n",
      "[ True] [-0.101229] [-0.101229]\n",
      "[ True] [-0.229119] [-0.229119]\n",
      "[ True] [-0.299019] [-0.299019]\n",
      "[ True] [-0.247055] [-0.247055]\n",
      "[ True] [-0.49922] [-0.49922]\n",
      "[ True] [-0.485892] [-0.485892]\n",
      "[ True] [-0.669503] [-0.669503]\n"
     ]
    }
   ],
   "source": [
    "# Checking equality of numbers\n",
    "\n",
    "data1 = np.round(new_data1, 6) # removing floating point error\n",
    "data2 = np.round(new_data2, 6) \n",
    "\n",
    "print(\"Is equal: \")\n",
    "for i, j in zip (data1, data2):\n",
    "    print(i == j, i, j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c3da197",
   "metadata": {},
   "source": [
    "As we can see, the results are the same."
   ]
  }
 ],
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