M2_SETI/D3/TP/TP_SETI_SVM/SVM.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP 3 SVM\n",
    "On se propose de faire de la modélisation par SVM sur des problématiques de discrimination, en utilisant la bibliothèque scikit-learn.\n",
    "\n",
    "On veut : \n",
    "- Traiter un problème de discrimination linéairement séparable\n",
    "- Traiter un problème non linéairement séparable (SVM à noyaux)\n",
    "- Traiter le problème de la discrimination de chiffres manuscrits"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problème linéairement séparable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.svm import SVC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "def genere_ex_1(n1=100, n2=50, mu1=[0,3], mu2=[3,0], sd1=0.15, sd2=0.2):\n",
    "    \"\"\" Génération de point\n",
    "    \"\"\"\n",
    "    X = np.concatenate((np.random.multivariate_normal(mu1, np.diagflat(sd1*np.ones(2)), n1),\n",
    "                        np.random.multivariate_normal(mu2, np.diagflat(sd2*np.ones(2)),n2)))\n",
    "\n",
    "    Y = np.concatenate((np.ones((n1,1)), -1*np.ones((n2,1))))[:,0]\n",
    "    return X,Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data_hyperplan(X, Y, classifier, name):\n",
    "    \"\"\" Affichage du classifieur \n",
    "    \"\"\"\n",
    "    w = classifier.coef_[0]\n",
    "    b = classifier.intercept_[0]\n",
    "    a = -w[0] / w[1]\n",
    "    xx = np.linspace(min(X[:,0]), max(X[:,0]))\n",
    "    yy = a * xx - b/w[1]\n",
    "\n",
    "    color = ['red' if c >= 0 else 'blue' for c in Y]\n",
    "    plt.scatter(X[:,0], X[:,1], color=color)\n",
    "\n",
    "    plt.plot(xx,yy, color='black')\n",
    "    plt.plot(xx, yy+1/w[1], color='green')\n",
    "    plt.plot(xx, yy-1/w[1], color='green')\n",
    "    plt.xlabel(\"x1\")\n",
    "    plt.ylabel(\"x2\")\n",
    "    plt.title(\"Classe 1 (red), Classe -1 (blue)\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "def main(X,Y):\n",
    "    classifier = SVC(kernel='linear', probability=True)\n",
    "    classifier = classifier.fit(X, Y)\n",
    "\n",
    "    plot_data_hyperplan(X, Y, classifier, 'Graph_SVM_linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y = genere_ex_1() \n",
    "main(X, Y)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problème non linéairement séparable\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "def genere_ex_2(n=300, mu=[0,0], std=0.25, delta=0.2):\n",
    "    \"\"\" Génération de données de nuage gaussien centré en 0 et traversé par une fonction polynomiale de degré 3\n",
    "    \"\"\"\n",
    "    X = np.random.multivariate_normal(mu, np.diagflat(std*np.ones(2)), n)\n",
    "    Y = np.zeros((X.shape[0]))\n",
    "\n",
    "    for i in range(X.shape[0]):\n",
    "        x = X[i,0]\n",
    "        y = X[i,1]\n",
    "        if y < x*(x-1)*(x+1):\n",
    "            Y[i] = -1\n",
    "            X[i,1] = X[i,1] - delta\n",
    "        else:\n",
    "            Y[i] = 1\n",
    "            X[i,1] = X[i,1] + delta\n",
    "    return X,Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(X,Y,classifier, nameFig):\n",
    "    \"\"\" Visualisation\n",
    "    \"\"\"\n",
    "    minx1 = min(X[:,0])\n",
    "    maxx1 = max(X[:,0])\n",
    "    minx2 = min(X[:,1])\n",
    "    maxx2 = max(X[:,1])\n",
    "\n",
    "    xx = np.linspace(minx1, maxx1, 100)\n",
    "    yy = np.linspace(minx2, maxx2, 100).T\n",
    "    xx, yy = np.meshgrid(xx,yy)\n",
    "    Xfull = np.c_[xx.ravel(), yy.ravel()]\n",
    "\n",
    "    probas = classifier.predict_proba(Xfull)\n",
    "    Z = classifier.decision_function(Xfull)\n",
    "\n",
    "    k = 1\n",
    "    plt.title(\"Class %d\" %k)\n",
    "    imshow_handle = plt.imshow(probas[:, k].reshape((100,100)), extent=(minx1, maxx1, minx2, maxx2), origin='lower')\n",
    "    \n",
    "    classPos = Y>=0\n",
    "    classNeg = Y<0\n",
    "\n",
    "    plt.contour(xx, yy, Z.reshape((100,100)), [-1,0,1], colors=['blue', 'black', 'red'])\n",
    "    plt.scatter(X[classPos, 0], X[classPos, 1], marker='o', c='r', edgecolors='k')\n",
    "    plt.scatter(X[classNeg, 0], X[classNeg, 1], marker='o', c='b', edgecolors='k')\n",
    "\n",
    "    ax = plt.axes([0.8, 0.15, 0.05, 0.7])\n",
    "\n",
    "    plt.title('Probability')\n",
    "    plt.colorbar(imshow_handle, cax=ax, orientation='vertical')\n",
    "    \n",
    "    plt.savefig(nameFig+'.jpg', dpi=300)\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "def main(X,Y,nameFig = 'GridSearchCV'):\n",
    "    \"\"\" Création du modèle avec la recherche du meilleur paramétrage de GridSearchCV \n",
    "    \"\"\"\n",
    "    parameters = {'kernel':('poly', 'poly'), 'C':[0.1,0.5, 1, 10], 'degree':[3,5], 'coef0':[0, 0.1, 0.5, 1, 10]}\n",
    "    svc = SVC(probability=True)\n",
    "    classifier = GridSearchCV(svc, parameters)\n",
    "    classifier = classifier.fit(X,Y)\n",
    "    print(classifier.best_params_)\n",
    "\n",
    "    plot(X,Y, classifier=classifier, nameFig=nameFig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'C': 1, 'coef0': 0.5, 'degree': 3, 'kernel': 'poly'}\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,Y = genere_ex_2()\n",
    "main(X,Y)"
   ]
  }
 ],
 "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": "3.9.4 (tags/v3.9.4:1f2e308, Apr  6 2021, 13:40:21) [MSC v.1928 64 bit (AMD64)]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "2ef431f6525756fa8a44688585fa332ef3b2e5fcfe8fe75df35bbf7028a8b511"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}