SVM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importe les Librairies\n",
    "from sklearn.svm import SVC\n",
    "from sklearn import datasets, model_selection, preprocessing, decomposition\n",
    "import svm_source\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mise en Oeuvre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Charge les données Iris\n",
    "scaler = preprocessing.StandardScaler()\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data\n",
    "X = scaler.fit_transform(X)\n",
    "y = iris.target\n",
    "X = X[y != 0, :2]\n",
    "y = y[y != 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Kernel Linéaire"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# definit un modèle SVM avec kernel linéaire\n",
    "clf_linear = SVC(kernel='linear',gamma='scale')\n",
    "clf_linear.fit(X, y)\n",
    "# plot la prediction du modèle\n",
    "plt.figure(figsize=(4,6))\n",
    "svm_source.frontiere(clf_linear.predict, X, y, step=100,colorbar=False)\n",
    "plt.title('linear kernel')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean score = 0.6834\n"
     ]
    }
   ],
   "source": [
    "# calcul la performance généralisée en divisant Xtrain/Xtest plusieurs fois \n",
    "n_iter = 100\n",
    "linear_scores = []\n",
    "for k in range(n_iter):\n",
    "    Xtrain, Xtest, Ytrain, Ytest = model_selection.train_test_split(X, y, test_size=0.5) # créer 2 échantillons 50%-50% aléatoirement choisi\n",
    "    clf_linear.fit(Xtrain, Ytrain)\n",
    "    linear_scores.append(clf_linear.score(Xtest,Ytest))\n",
    "print(\"mean score = \" + str(np.mean(linear_scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Kernel Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# definit un modèle SVM avec kernel linéaire\n",
    "plt.figure(figsize=(4,6))\n",
    "clf_pol = SVC(kernel='poly',gamma='scale') # on garde les hyperparametres par défaut (degree=3, coef0=0)\n",
    "clf_pol.fit(Xtrain, Ytrain)\n",
    "# plot la prediction du modèle\n",
    "svm_source.frontiere(clf_pol.predict, Xtrain, Ytrain, step=100,colorbar=False)\n",
    "plt.title('polynomial kernel')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean score = 0.5856\n"
     ]
    }
   ],
   "source": [
    "# calcul la performance généralisée en divisant Xtrain/Xtest plusieurs fois \n",
    "clf_poly = SVC(kernel='poly',gamma='scale')\n",
    "n_iter = 100\n",
    "poly_scores = []\n",
    "for k in range(n_iter):\n",
    "    Xtrain, Xtest, Ytrain, Ytest = model_selection.train_test_split(X, y, test_size=0.5) # créer 2 échantillons 50%-50% aléatoirement choisi\n",
    "    clf_poly.fit(Xtrain, Ytrain)\n",
    "    poly_scores.append(clf_poly.score(Xtest,Ytest))\n",
    "print(\"mean score = \" + str(np.mean(poly_scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\underline{\\text{conclusion:}}  \\text{ Rendre le modèle plus complexe ne donne pas forcément une meilleur performance. }$\n",
    "\n",
    "$\\text{Pour aller plus loin avec le kernel polynomial, il faudrait chercher à optimiser les hyperparamètres (degree et coef0) du modèle.}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\underline{\\text{problème primal SVM : }}$ \n",
    "$$\\min_{w,w_0} \\frac{1}{2}||w||^2 + C \\sum_{i=1}^n \\xi_i \\\\\n",
    "\\text{sc } \\forall i,\\ y_i(w^T\\Phi(x_i)+w_0) \\geq 1 - \\xi_i\\ \\text{ et } \\xi_i \\geq 0 $$\n",
    "\n",
    "$\\text{Dans le problème de minimisation, on veut que } \\sum_i^n \\xi_i \\text{ soit minimale.}$\n",
    "\n",
    "$\\text{Et, on veut également que les } \\xi_i \\text{ respectent les contraintes :}$ \n",
    "\n",
    "$ \\quad \\quad  y_i(w^T\\Phi(x_i)+w_0) \\geq 1 - \\xi_i \\text{ et } \\xi_i \\geq 0 $\n",
    "\n",
    "$ \\implies     1 - y_i(w^T\\Phi(x_i)+w_0) \\leq \\xi_i \\text{ et } 0 \\leq \\xi_i$\n",
    "\n",
    "$\\text{Les plus petits $\\xi_i$ qui vérifient les contraintes sont donc } \\xi_i = \\max\\left(0,1 - y_i(w^T\\Phi(x_i)+w_0)\\right) $\n",
    "\n",
    "$\\text{d'où,}$\n",
    "        $$\\min_{w,w_0} \\frac{1}{2}||w||^2 + C \\sum_{i=1}^n [1-y_i(w^T\\Phi(x_i)+w_0)]_+ $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "y = np.linspace(-2, 2, 1000)\n",
    "plt.plot(y, y < 0,label='$\\mathbb{1}(y_if(x_i)<0)$')\n",
    "plt.plot(y, np.maximum(0, 1 - y),label='$\\max(0,1 - y_if(x_i)$')\n",
    "plt.legend(fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\max(0,1 - y_if(x_i) \\text{ est bien un majorant convexe de } \\mathbb{1}y_if(x_i)<0$\n",
    "\n",
    "$\\text{Et, on a les 3 cas:}$\n",
    "\n",
    "$\\text{   $y_if(x_i) > 1$ , le point est \"en dehors\" de la marge. (pas de contribution à la pénalisation)}$\n",
    "\n",
    "$\\text{   $y_if(x_i) = 1$ , le point est  sur la marge}$\n",
    "\n",
    "$\\text{   $y_if(x_i) < 1$ , le point est \"à l'intérieur\" de la marge. (contribution à la pénalisation)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVM GUI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](SVM_GUI.png)\n",
    "\n",
    "$\\text{ Quand C diminue, alors la marge augmente (et les erreurs de classification également).}$\n",
    "\n",
    "$\\text{ Pour un cas où les classes sont déséquilibrées, ce phénomène est également visible et les points de la classe en sous nombres finissent par être }$\n",
    "\n",
    "$\\text{ tous mal classé par la SVM.}$\n",
    "\n",
    "$\\longrightarrow \\text{ On peut corriger ce phénomène en mettant un poids élevé sur ces points là.}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification de visages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Charge les données\n",
    "lfw_people = datasets.fetch_lfw_people(min_faces_per_person=200) # garde les 2 classes qui ont plus de 140 observations\n",
    "n_samples, h, w = lfw_people.images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalise\n",
    "X = lfw_people.data\n",
    "X = preprocessing.StandardScaler().fit_transform(X)\n",
    "y = lfw_people.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x360 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot quelques exemples\n",
    "plt.figure(figsize=(17, 5))\n",
    "plt.suptitle(\"Images Examples\")\n",
    "for i in range(5):\n",
    "    plt.subplot(1, 5, i + 1)\n",
    "    image_k = np.random.randint(n_samples)\n",
    "    plt.imshow(X[image_k].reshape((h, w)), cmap=plt.cm.gray)\n",
    "    plt.title(lfw_people.target_names[lfw_people.target[image_k]], size=12)\n",
    "    plt.xticks(())\n",
    "    plt.yticks(())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\text{Si on ne réduisait pas nos données, alors on ne pénalerisait pas de la même façon toute les variables.}$\n",
    "       \n",
    "$\\text{Et il faut centrer pour ne pas pénaliser l'intercept.}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 6\n",
    "Montrez l’influence du paramètre de régularisation : afficher l’erreur de\n",
    "prédiction en fonction de $C$ sur une échelle logarithmique entre $10^{-5}$ et $10^5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# divise en ensemble Train/Test\n",
    "X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "# Evolution du score (kernel linéaire) en fonction de l'hyperparametre C\n",
    "scores = []\n",
    "C_grid = np.logspace(-5,-1,num=30)\n",
    "for C_value in C_grid:\n",
    "    clf = SVC(kernel='linear',C=C_value,gamma='scale')\n",
    "    clf = clf.fit(X_train, y_train)\n",
    "    scores.append(clf.score(X_test,y_test))\n",
    "    \n",
    "plt.figure()\n",
    "plt.plot(C_grid,scores,'-')\n",
    "plt.xscale('log'),plt.xlabel('C'),plt.ylabel('score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C_opt_linear =  {'C': 0.0006210169418915617}\n",
      "score_linear =  0.9322916666666666\n"
     ]
    }
   ],
   "source": [
    "# Confirme la valeur du C optimal avec GridSearchCV\n",
    "clf_linear = model_selection.GridSearchCV(SVC(kernel='linear',gamma='scale'), {'C': C_grid}, cv=5, iid=False)\n",
    "clf_linear.fit(X_train, y_train)\n",
    "print(\"C_opt_linear = \",clf_linear.best_params_)\n",
    "print(\"score_linear = \",clf_linear.score(X_test,y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 7\n",
    "En ajoutant des variables de nuisances (par exemple 300 variables normales centrées réduites),\n",
    "augmentant ainsi le nombre de variables à nombre de points d’apprentissage fixé, montrez que la\n",
    "performance chute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "# ajout de 300 X random dans nos données\n",
    "noise_train = np.random.randn(X_train.shape[0], 300)\n",
    "X_train2 = np.concatenate((X_train, noise_train), axis=1)\n",
    "noise_test = np.random.randn(X_test.shape[0], 300)\n",
    "X_test2 = np.concatenate((X_test, noise_test), axis=1)\n",
    "# Affiche l'évolution de la performance avec C\n",
    "scores = []\n",
    "for C_value in C_grid:\n",
    "    clf = SVC(kernel='linear',C=C_value,gamma='scale')\n",
    "    clf = clf.fit(X_train2, y_train)\n",
    "    scores.append(clf.score(X_test2,y_test))\n",
    "    \n",
    "plt.figure()\n",
    "plt.plot(C_grid,scores,'-')\n",
    "plt.xscale('log'), plt.xlabel('C'), plt.ylabel('score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score_noise =  0.9322916666666666\n"
     ]
    }
   ],
   "source": [
    "# Confirme la valeur du C optimal avec GridSearchCV\n",
    "clf_noise = model_selection.GridSearchCV(SVC(kernel='linear',gamma='scale'), {'C': C_grid}, cv=5, iid=False)\n",
    "clf_noise.fit(X_train2, y_train)\n",
    "print(\"score_noise = \",clf_noise.score(X_test2,y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\longrightarrow \\text{ En ajoutant des variables de bruits, le score a baissé. }$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score_pca =  0.9322916666666666\n"
     ]
    }
   ],
   "source": [
    "# Decomposition PCA\n",
    "n_components = 150 # les autres composantes ont des valeurs propres proches de 0\n",
    "pca = decomposition.PCA(n_components=n_components).fit(X_train2)\n",
    "\n",
    "# Projette les données\n",
    "X_train_pca = pca.transform(X_train2)\n",
    "X_test_pca = pca.transform(X_test2)\n",
    "\n",
    "clf = model_selection.GridSearchCV(SVC(kernel='linear',gamma='scale'), {'C': C_grid}, cv=5, iid=False)\n",
    "clf.fit(X_train_pca, y_train)\n",
    "print(\"score_pca = \",clf.score(X_test_pca,y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\longrightarrow \\text{ La performance ne s'est pas amélioré mais la vitesse de convergence a diminué.} $ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score_rbf =  0.6927083333333334\n"
     ]
    }
   ],
   "source": [
    "clf_rbf = model_selection.GridSearchCV(SVC(kernel='rbf',gamma='scale'), {'C': C_grid}, cv=5, iid=False)\n",
    "clf_rbf.fit(X_train2, y_train)\n",
    "print(\"score_rbf = \",clf_rbf.score(X_test2,y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\longrightarrow \\text{ La performance a diminué (complexité n'implique pas meilleur prédiction).} $ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pour aller plus loin : Calcul du saut de dualité\n",
    "En vous basant sur cet exemple écrivez un code qui va calculer la valeur des fonctionnelles primales\n",
    "et duales et vérifiez que les valeurs sont proches. Comment varie la différence entre les deux valeurs\n",
    "quand on fait varier la tolérance sur l’optimisation (paramètre tol de SVC) ? Vous afficherez la\n",
    "différence des valeurs des fonctionnelles.\n",
    "\n",
    "$$fct_{primal} = \\frac{1}{2} ||w||^2 + C \\sum_i^n \\xi_i$$\n",
    "\n",
    "$$ $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "C = 1e-3\n",
    "tol_values =  np.logspace(-5,-1,num=20)\n",
    "dual_gaps = []\n",
    "for tol_value in tol_values:\n",
    "    # calcul le modèle SVM\n",
    "    clf_linear = SVC(kernel='linear', C=C, gamma='scale',tol=tol_value)\n",
    "    clf_linear = clf_linear.fit(X_train, y_train)\n",
    "    # calcul la valeur de la fonction primale\n",
    "    w = clf_linear.coef_\n",
    "    b = clf_linear.intercept_\n",
    "    xi = 1 - y_train * (np.dot(w,X_train.T) + b)\n",
    "    fct_primal = 1/2 * np.dot(w,w.T) + C * np.sum(xi)\n",
    "    # calcul la valeur de la fonction duale\n",
    "    alpha = clf_linear.dual_coef_.T\n",
    "    x_support = X_train[clf_linear.support_]\n",
    "    y_support = y_train[clf_linear.support_]\n",
    "    fct_dual = sum(alpha) + (-1/2) * sum([alpha[i] * alpha[j] * y_support[i] * y_support[j] * np.dot(x_support[i], x_support[j]) for i in range(x_support.shape[0]) for j in range(x_support.shape[0])])\n",
    "    \n",
    "    dual_gaps.append(np.squeeze(abs(fct_dual-fct_primal)))\n",
    "\n",
    "    \n",
    "\n",
    "# Plot gap de dualité en fonction de la tolérance\n",
    "plt.figure()\n",
    "plt.plot(tol_values, dual_gaps, '-')\n",
    "plt.xlabel('tolérance'), plt.ylabel('saut de dualité')\n",
    "plt.xscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\longrightarrow  \\text{Quand la tolérance diminue, la différence de valeur entre les fonctions primales et duales diminuent également.}$\n",
    "\n",
    "$ \\text{(sûrement dû à une convergence numérique dans les algorithmes de minimisation)}$"
   ]
  }
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