teaching/testLDA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [],
   "source": [
    "x1 = [0, -1, -2, -1, 1/2, 1, 1, 3/2]\n",
    "x2 = [-1, -1/2, -1, -3/2, 1, 2, 0, 1]\n",
    "\n",
    "X = np.array([x1, x2]).T\n",
    "y = np.array([0, 0, 0, 0, 1, 1, 1, 1])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [],
   "source": [
    "df = pd.DataFrame(X, columns=['x1', 'x2'])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [],
   "source": [
    "df['y'] = y"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "    x1   x2  y\n0  0.0 -1.0  0\n1 -1.0 -0.5  0\n2 -2.0 -1.0  0\n3 -1.0 -1.5  0\n4  0.5  1.0  1\n5  1.0  2.0  1\n6  1.0  0.0  1\n7  1.5  1.0  1",
      "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>x1</th>\n      <th>x2</th>\n      <th>y</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.0</td>\n      <td>-1.0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>-1.0</td>\n      <td>-0.5</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>-2.0</td>\n      <td>-1.0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-1.0</td>\n      <td>-1.5</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.5</td>\n      <td>1.0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1.0</td>\n      <td>2.0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1.0</td>\n      <td>0.0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1.5</td>\n      <td>1.0</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 558.875x500 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='x1', y='x2', data=df, hue='y', fit_reg=False, scatter_kws={\"s\": 100})\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [],
   "source": [
    "# Calculate the means of the two classes\n",
    "mean_0 = np.mean(X[y==0], axis=0)\n",
    "mean_1 = np.mean(X[y==1], axis=0)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([-1., -1.]), array([1., 1.]))"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_0, mean_1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [],
   "source": [
    "# Calculate the pi0, pi1\n",
    "pi0 = np.sum(y==0) / len(y)\n",
    "pi1 = np.sum(y==1) / len(y)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "(0.5, 0.5)"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi0, pi1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [],
   "source": [
    "# Calculate the covariance matrix\n",
    "cov_0 = np.zeros((2, 2))\n",
    "cov_1 = np.zeros((2, 2))\n",
    "\n",
    "for i in range(len(y)):\n",
    "    if y[i] == 0:\n",
    "        cov_0 += np.outer(X[i] - mean_0, X[i] - mean_0)\n",
    "    else:\n",
    "        cov_1 += np.outer(X[i] - mean_1, X[i] - mean_1)\n",
    "\n",
    "cov_0 /= np.sum(y==0)\n",
    "cov_1 /= np.sum(y==1)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0.5  , 0.   ],\n       [0.   , 0.125]])"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_0"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0.125, 0.   ],\n       [0.   , 0.5  ]])"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [],
   "source": [
    "# calculate the covariance matrix general\n",
    "cov = (pi0 * cov_0 + pi1 * cov_1)/len(y)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0.0390625, 0.       ],\n       [0.       , 0.0390625]])"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [],
   "source": [
    "# Calculate the inverse of the covariance matrix\n",
    "cov_inv = np.linalg.inv(cov)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [],
   "source": [
    "# Calculate the weights\n",
    "w = np.dot(cov_inv, (mean_0 - mean_1))\n",
    "# Calculate the bias\n",
    "b = -0.5 * np.dot(np.dot(mean_0.T, cov_inv), mean_0) + 0.5 * np.dot(np.dot(mean_1.T, cov_inv), mean_1) + np.log(pi0/pi1)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([-51.2, -51.2]), 0.0)"
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w, b"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 558.875x500 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the decision boundary\n",
    "x1 = np.linspace(-2, 2, 100)\n",
    "x2 = -(w[0] * x1 + b) / w[1]\n",
    "\n",
    "# Plot the decision boundary\n",
    "sns.lmplot(x='x1', y='x2', data=df, hue='y', fit_reg=False, scatter_kws={\"s\": 100})\n",
    "plt.plot(x1, x2, color='black')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of x = [1/2, 1/2] is:  5.809282904332702e-23\n",
      "Class 0\n"
     ]
    }
   ],
   "source": [
    "# Predict the class of x = [1/2, 1/2]\n",
    "x = np.array([1/2, 1/2])\n",
    "y_pred = np.dot(x, w) + b\n",
    "print('Probability of x = [1/2, 1/2] is: ', 1/(1 + np.exp(-y_pred)))\n",
    "if y_pred > 0:\n",
    "    print('Class 1')\n",
    "else:\n",
    "    print('Class 0')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 558.875x500 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='x1', y='x2', data=df, hue='y', fit_reg=False, scatter_kws={\"s\": 100})\n",
    "plt.plot(x1, x2, color='black')\n",
    "plt.scatter(x[0], x[1], color='green', s=200)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [],
   "source": [
    "# With mu_0 = [-1, -1, -1], mu_1 = [1, 1, 1], pi0 = 0.5, pi1 = 0.5\n",
    "mu_0 = np.array([-1, -1, -1])\n",
    "mu_1 = np.array([1, 1, 1])\n",
    "pi0 = 0.5\n",
    "pi1 = 0.5\n",
    "sigma = np.array([[2, 1, 1], [1, 1, 2], [1, 2, 2]])\n",
    "\n",
    "# Calculate the weights\n",
    "w = np.dot(np.linalg.inv(sigma), (mu_0 - mu_1))\n",
    "\n",
    "# Calculate the bias\n",
    "b = -0.5 * np.dot(np.dot(mu_0.T, np.linalg.inv(sigma)), mu_0) + 0.5 * np.dot(np.dot(mu_1.T, np.linalg.inv(sigma)), mu_1) + np.log(pi0/pi1)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [
    {
     "data": {
      "text/plain": "(array([-0.66666667,  0.        , -0.66666667]), 0.0)"
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w, b"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of x_test is:  0.33924363123418283\n",
      "Class 0\n"
     ]
    }
   ],
   "source": [
    "# Predict the class of x_test\n",
    "x_test = np.array([1, 0, 0])\n",
    "y_pred = np.dot(x_test, w) + b\n",
    "print('Probability of x_test is: ', 1/(1 + np.exp(-y_pred)))\n",
    "if y_pred > 0:\n",
    "    print('Class 1')\n",
    "else:\n",
    "    print('Class 0')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}