Multi Class Gaussian Discriminant Analyses.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np   \n",
    "\n",
    "class GDAClassifier:\n",
    "    \n",
    "    def fit(self, X, y, epsilon = 1e-10):\n",
    "        self.y_classes, y_counts = np.unique(y, return_counts=True)\n",
    "        self.phi_y = 1.0 * y_counts/len(y)\n",
    "        self.u = np.array([ X[y==k].mean(axis=0) for k in self.y_classes])\n",
    "        self.E = self.compute_sigma(X, y)\n",
    "        self.E += np.ones_like(self.E) * epsilon # fix zero overflow\n",
    "        self.invE = np.linalg.pinv(self.E)\n",
    "        return self\n",
    "    \n",
    "    def compute_sigma(self,X, y):\n",
    "        X_u = X.copy().astype('float64')\n",
    "        for i in range(len(self.u)):\n",
    "            X_u[y==self.y_classes[i]] -= self.u[i]\n",
    "        return X_u.T.dot(X_u) / len(y)\n",
    "\n",
    "    def predict(self, X):\n",
    "        return np.apply_along_axis(self.get_prob, 1, X)\n",
    "    \n",
    "    def score(self, X, y):\n",
    "        return (self.predict(X) == y).mean()\n",
    "    \n",
    "    def get_prob(self, x):\n",
    "        p = np.exp(-0.5 * np.sum((x - self.u).dot(self.invE) * (x - self.u), axis =1)) * self.phi_y\n",
    "        print(p)\n",
    "        return np.argmax(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import train_test_split\n",
    "from sklearn.datasets import load_iris\n",
    "X,y = load_iris(return_X_y=True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, test_size=0.8)\n",
    "model = GDAClassifier().fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9833333333333333"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9296703296703297"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "X,y = load_breast_cancer(return_X_y=True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, test_size=0.8)\n",
    "model = GDAClassifier().fit(X_train,y_train)\n",
    "model.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      " 8.22710729e-30 7.47483788e-26]\n",
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      " 4.21511848e-18 2.08368322e-23]\n",
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      " 1.91356164e-43 1.27456863e-43]\n",
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      " 1.87144502e-22 4.23349007e-18 6.16662446e-23 2.92509935e-21\n",
      " 2.51399858e-15 4.44953322e-13]\n",
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      " 2.35470131e-11 6.67421949e-16]\n",
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      " 9.74291506e-19 9.00170339e-21]\n",
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      " 2.59254576e-27 2.66909582e-18 3.97689424e-23 2.45279557e-27\n",
      " 1.32754019e-22 1.39637439e-23]\n",
      "[1.45876028e-33 5.69719002e-22 2.03294049e-37 2.36083418e-35\n",
      " 1.78777238e-13 2.89391150e-34 6.69810895e-25 1.28460519e-30\n",
      " 1.15399513e-27 2.07575381e-32]\n",
      "[1.13235930e-19 7.20755314e-17 1.57129836e-26 1.23897066e-21\n",
      " 2.44380854e-22 8.02052977e-21 4.50504919e-21 1.83445406e-22\n",
      " 2.78145074e-13 1.47927554e-16]\n",
      "[2.06112531e-25 3.14985776e-17 6.39976445e-21 1.84124835e-27\n",
      " 2.95195241e-25 9.07889543e-27 7.61143138e-15 1.90356114e-29\n",
      " 9.55847369e-19 1.57672065e-25]\n",
      "[3.88696172e-22 8.81319215e-24 1.58399704e-31 2.74515500e-24\n",
      " 7.14927574e-25 5.18460063e-24 1.47995551e-08 9.87628968e-30\n",
      " 2.01246803e-20 1.12913301e-24]\n",
      "[1.69251635e-25 3.94288931e-18 4.12546824e-19 2.00232027e-08\n",
      " 1.82981864e-30 5.46330494e-18 1.08935273e-22 1.51139187e-21\n",
      " 5.92408743e-16 1.17853597e-14]\n",
      "[2.22479150e-19 1.89283507e-19 7.10628450e-26 3.00875940e-22\n",
      " 8.85642417e-18 5.38824057e-22 6.22739474e-05 4.51503176e-25\n",
      " 3.45031951e-17 1.28149172e-22]\n",
      "[3.52662288e-26 1.79110529e-21 2.12771376e-22 2.48588589e-16\n",
      " 2.76437239e-29 3.23777057e-13 3.93292946e-19 7.29029882e-24\n",
      " 4.46184048e-18 6.91699407e-14]\n",
      "[2.35673334e-35 1.12902691e-27 2.42375414e-28 1.58942192e-23\n",
      " 6.36416052e-30 2.33778023e-24 6.38112851e-34 7.59573963e-11\n",
      " 1.75759041e-26 1.99711227e-23]\n",
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      " 2.43511289e-36 3.08621110e-23 3.22967602e-28 5.09099296e-27\n",
      " 9.83763615e-20 1.56282946e-20]\n",
      "[2.44548519e-26 2.18922307e-10 1.22071451e-18 5.81544010e-19\n",
      " 7.32258790e-21 3.46401684e-22 1.50148777e-20 1.05480351e-18\n",
      " 5.18461729e-12 8.25421439e-18]\n",
      "[2.80159661e-29 4.84807666e-20 1.25099354e-25 2.95687921e-19\n",
      " 2.34691773e-25 2.79491689e-19 1.55188336e-29 1.19106454e-08\n",
      " 7.96812571e-20 2.75548031e-16]\n",
      "[1.39480800e-209 1.67868523e-200 4.50477029e-210 1.09514910e-210\n",
      " 8.66677463e-185 8.80382700e-207 1.55905130e-199 2.80052478e-206\n",
      " 4.62128971e-202 8.32713663e-207]\n",
      "[6.20615593e-36 3.71898924e-33 6.75519420e-43 1.35604125e-39\n",
      " 2.87043954e-31 1.50531717e-33 4.52069630e-35 1.63925770e-28\n",
      " 1.34616017e-32 1.86757871e-33]\n",
      "[7.16647783e-28 3.32494445e-27 5.70430317e-29 4.46832758e-22\n",
      " 1.44103765e-28 1.07925424e-10 3.93300504e-26 1.91913749e-20\n",
      " 6.90382802e-25 2.52762825e-20]\n",
      "[1.93670053e-07 1.45056308e-23 6.18633563e-24 3.50896275e-22\n",
      " 8.00055056e-24 1.81797745e-20 1.05884586e-18 2.52209409e-25\n",
      " 4.02026003e-19 5.31063289e-17]\n",
      "[4.21056569e-29 4.96758874e-21 3.65023876e-28 1.49841956e-20\n",
      " 2.13725303e-24 1.40802095e-20 3.23491494e-27 7.17256819e-08\n",
      " 5.37044785e-20 5.09186853e-19]\n",
      "[2.48124747e-36 1.72872823e-21 1.28681278e-28 6.31600492e-25\n",
      " 1.26352464e-32 7.87667883e-18 1.05089995e-31 5.39938675e-23\n",
      " 6.30383720e-24 2.55012782e-25]\n",
      "[9.40299982e-25 6.90086941e-23 2.34712130e-33 2.14669884e-34\n",
      " 1.62149499e-08 8.27069475e-29 8.79977499e-19 3.71338155e-26\n",
      " 1.38278820e-26 2.09223432e-28]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.965478841870824"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "X = digits.data\n",
    "y = digits.target\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, test_size=0.5)\n",
    "model = GDAClassifier().fit(X,y)\n",
    "model.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e-10,  1.00000000e-10,  1.00000000e-10, ...,\n",
       "         1.00000000e-10,  1.00000000e-10,  1.00000000e-10],\n",
       "       [ 1.00000000e-10,  6.85260934e-01,  1.31558591e+00, ...,\n",
       "        -2.49550674e-01, -1.72916333e-01, -1.47619408e-01],\n",
       "       [ 1.00000000e-10,  1.31558591e+00,  1.24547655e+01, ...,\n",
       "        -1.46806270e+00, -3.44024003e-02,  3.11114596e-01],\n",
       "       ...,\n",
       "       [ 1.00000000e-10, -2.49550674e-01, -1.46806270e+00, ...,\n",
       "         1.83142211e+01,  7.67224211e+00,  1.55782058e+00],\n",
       "       [ 1.00000000e-10, -1.72916333e-01, -3.44024003e-02, ...,\n",
       "         7.67224211e+00,  1.09016392e+01,  3.41868286e+00],\n",
       "       [ 1.00000000e-10, -1.47619408e-01,  3.11114596e-01, ...,\n",
       "         1.55782058e+00,  3.41868286e+00,  2.99539167e+00]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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   "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": "2.7.16"
  }
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