Multilayer perceptron.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "id": "Lp_bWhjIL-kq"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "id": "saCXjzSIL-kr",
    "notebookRunGroups": {
     "groupValue": ""
    }
   },
   "outputs": [],
   "source": [
    "def generate_data_3classes(n1,n2,n3, display=True):\n",
    "    X1 = np.random.randn(n1,2)*0.15 - np.array([0.2 , 0.2])\n",
    "    X2 = np.random.randn(n2,2)*0.25 + np.array([0.1 , 0.5])\n",
    "    X3 = np.random.randn(n3,2)*0.15 + np.array([0.6 , 0.2])\n",
    "    X = np.concatenate((X1,X2,X3), axis=0)\n",
    "    Y = np.concatenate([np.ones(n1), np.ones(n2)*2, np.ones(n3)*3])-1\n",
    "\n",
    "    if display:\n",
    "        plt.plot(X1[:,0], X1[:,1], '.r')\n",
    "        plt.plot(X2[:,0], X2[:,1], '.g')\n",
    "        plt.plot(X3[:,0], X3[:,1], '.b')\n",
    "        plt.show()\n",
    "\n",
    "    return X,Y\n",
    "\n",
    "#Converts a class vector (integers) to binary class matrix (copy from keras)\n",
    "def to_categorical(y, num_classes=None, dtype=\"float32\"):\n",
    "    y = np.array(y, dtype=\"int\")\n",
    "    input_shape = y.shape\n",
    "    if input_shape and input_shape[-1] == 1 and len(input_shape) > 1:\n",
    "        input_shape = tuple(input_shape[:-1])\n",
    "    y = y.ravel()\n",
    "    if not num_classes:\n",
    "        num_classes = np.max(y) + 1\n",
    "    n = y.shape[0]\n",
    "    categorical = np.zeros((n, num_classes), dtype=dtype)\n",
    "    categorical[np.arange(n), y] = 1\n",
    "    output_shape = input_shape + (num_classes,)\n",
    "    categorical = np.reshape(categorical, output_shape)\n",
    "    return categorical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "id": "YGIM2D2xL-ks",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0.]\n",
      " [1. 0. 0.]\n",
      " [1. 0. 0.]\n",
      " ...\n",
      " [0. 0. 1.]\n",
      " [0. 0. 1.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "X_train, Y_train = generate_data_3classes(100, 200, 150)\n",
    "Y_cat = to_categorical(Y_train)\n",
    "\n",
    "K=Y_cat.shape[1] #nombre de classes\n",
    "(num_examples,D) = X_train.shape # nombre d'exemples et dimension des exemples\n",
    "\n",
    "print(Y_cat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "id": "J7bCUy_jL-ks"
   },
   "outputs": [],
   "source": [
    "# fonction sigmoide\n",
    "def sigmo(v):\n",
    "    return 1/(1+math.e**(-v))\n",
    "\n",
    "# dérivée de la fonction sigmoide\n",
    "def sigmop(v):\n",
    "    return math.e**(-v)/((1+math.e**(-v))**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "id": "cfb_040kL-kt"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(450, 2)"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initialisation aléatoire des poids\n",
    "W = 1 * np.random.normal(size=(D,K))\n",
    "b = np.zeros((1,K))\n",
    "\n",
    "# paramètres de l'apprentissage\n",
    "step_size = 1e-1\n",
    "num_iter = 10000\n",
    "\n",
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "id": "2fmP9q-XL-kt",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0: loss 0.2049253029720513\n",
      "iteration 1000: loss 0.041371889895716656\n",
      "iteration 2000: loss 0.04097574584692503\n",
      "iteration 3000: loss 0.04083805661524867\n",
      "iteration 4000: loss 0.04077765467833177\n",
      "iteration 5000: loss 0.040753940803335255\n",
      "iteration 6000: loss 0.04075218404946174\n",
      "iteration 7000: loss 0.04076543070427842\n",
      "iteration 8000: loss 0.040789594391397094\n",
      "iteration 9000: loss 0.040821756318611596\n",
      "[[-13.37824225  -6.27531008  34.87351413]\n",
      " [-24.04683779  13.23630395 -13.63677859]]\n",
      "(2, 3)\n"
     ]
    }
   ],
   "source": [
    "# Apprenttissage du réseau\n",
    "X = X_train\n",
    "Y = Y_cat\n",
    "\n",
    "# propagation\n",
    "for i in range(num_iter):\n",
    "\n",
    "    v = np.dot(X,W)+b\n",
    "    y_pred = sigmo(v)\n",
    "    error = y_pred - Y\n",
    "    loss = error**2\n",
    "    loss = np.mean(loss)\n",
    "    \n",
    "    if i % 1000 == 0:   \n",
    "        print('iteration {}: loss {}'.format(i, loss))\n",
    "\n",
    "    #retro-propagation\n",
    "\n",
    "    h = (error*sigmop(v)).T\n",
    "    dL_W =  (2*np.dot(h,X)).T\n",
    "    dL_b =  2*np.mean(error,axis=0)\n",
    "\n",
    "    \n",
    "    W = np.add(W, (-step_size * dL_W))\n",
    "    b = np.add(b, (-step_size * dL_b))\n",
    "\n",
    "print(W)\n",
    "print(dL_W.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "id": "Bktl0_orL-kt"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy: 0.95\n"
     ]
    }
   ],
   "source": [
    "# calcul de la précision\n",
    "v = np.dot(X,W)+b\n",
    "\n",
    "Y_pred = sigmo(v)\n",
    "class_pred = np.argmax(Y_pred,axis=1)\n",
    "\n",
    "print('Training accuracy: {:.2}'.format(np.mean(class_pred == Y_train)))"
   ]
  }
 ],
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