778 lines
19 KiB
Text
778 lines
19 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Introduction\n",
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"\n",
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"## Définitions\n",
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"\n",
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"La **matrice de confusion** est un tableau où on décompte les valeurs réelle O et prédites S pour chaque observation du jeu de données dans un problème de classification. Par sa conception, on peut valider rapidement le nombre d'observations où la prédiction est égale à la valeur réelle sur la diagonale de la matrice. Par convention, on place les valeurs prédites à la verticale et les valeurs observées à l'horizontale. Lorsque le nombre de modalités de la variable prédite est de deux, on a un problème de classification binaire et on obtient alors le décompte des vrais positifs, faux positifs, faux négatifs et vrais négatifs.\n",
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"\n",
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"La **précision** correspont à la proportion d'observations où la prédiction et la valeur réelle est dans une même classe par rapport au nombre d'observations où la prédiction est dans cette classe\n",
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"\n",
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"$$ \\text{Précision}_c = \\frac{\\sum_{i=1}^N 1_{s_i=c}1_{o_i=c}}{\\sum_{i=1}^N 1_{s_i=c}}$$\n",
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"\n",
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"Le **rappel** correspond à la proportions d'observations où la prédiction est dans une classe par rapport au nombre d'observations où la valeur réelle est dans cette classe.\n",
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"\n",
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"$$ \\text{Rappel}_c = \\frac{\\sum_{i=1}^N 1_{s_i=c}}{\\sum_{i=1}^N 1_{o_i=c}}$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Librairies utilisées\n",
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"\n",
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"Le project actuel est programmé dans le langage Python 3, et ce rapport est produit à l'aide de Jupyter Notebook. Seule les librairie standard `numpy` et `math` est utilisée, les autres ont été développées dans le cadre de ce projet."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Librairies standard\n",
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"import numpy as np\n",
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"import math\n",
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"# Librairies développées par l'étudiant\n",
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"import load_datasets as ld\n",
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"import BayesNaif\n",
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"import Knn\n",
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"import metrics"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Jeux de données\n",
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"\n",
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"Ce projet utilise 3 jeux de données: [Iris](https://archive.ics.uci.edu/ml/datasets/Iris), [MONKS](https://archive.ics.uci.edu/ml/datasets/MONK's+Problems) et [Congressional Voting Records Dataset](https://archive.ics.uci.edu/ml/datasets/Congressional+Voting+Records)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Algorithme des k plus proches voisins (kNN)\n",
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"\n",
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"Dans cette section, on présente les résultats obtenus pour l'algorithme des k plus proches voisins. Ce n'est pas un algorithme d'apprentissage à proprement parler, car il n'y a aucun modèle d'entrainé. On prédit la classe d'un nouvel élément en recherchant les k plus proches voisins selon une métrique choisie. Dans notre cas, nous utiliserons la distance de Minkowski, qui est une généralisation de la distance euclidienne et de la distance de Manhattan à l'aide d'un paramètre p. \n",
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"\n",
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"$${\\displaystyle D\\left(X,Y\\right)=\\left(\\sum _{i=1}^{N}|o_{i}-s_{i}|^{p}\\right)^{1/p}}$$\n",
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"\n",
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"On peut ainsi itérer sur différentes valeurs de ce paramètre pour trouver la mesure la plus adaptée au problème, tout en réutilisant la même fonction. Cette métrique s'utilise aurant pour des domaines de valeurs continus que discrets.\n",
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"\n",
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"## Pseudocode\n",
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"\n",
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"- Entrainement\n",
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"\n",
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"```\n",
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"Copier le jeu d'entrainement et les étiquettes d'entrainement dans la mémoire du modèle\n",
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"```\n",
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"\n",
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"- Prédiction Knn\n",
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"```\n",
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"Pour une observation x_i:\n",
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" Entrainement <- Vrai si on fait le premier entrainement\n",
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" T = copie jeu d'entrainement\n",
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" L = copie des étiquettes d'entrainement\n",
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" K = tableau de paires (point, distance) de longueur k\n",
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" Si Entrainement:\n",
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" Enlever x de T et l'étiquette de x_i de L\n",
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" Pour chaque observation t_j, j=[1,k]) de T:\n",
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" d(x_i,t_i) = distance de Minkowski entre x_i et t_j\n",
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" K[j] <- (t_i,d(x_i,t_j)) \n",
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" Pour chaque observation t_j, j=[k+1,N-1] de T:\n",
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" d(x,t_i) = distance de Minkowski entre x_i et t_j\n",
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" d_max <- distance maximum dans K\n",
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" pos_d_max <- position de d_max dans K\n",
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" Si d(x_i,t_j) < d_max\n",
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" Remplacer le point K[pos_d_max] par (t_j,d(x,t_j))\n",
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" s <- mode des valeurs des étiquettes des points dans K\n",
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" retourner s\n",
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"```\n",
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"\n",
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"- Test\n",
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"\n",
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"```\n",
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"Pour chaque observation x_i, i=1,N:\n",
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" S_i <- Prédiction(x_i)\n",
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"M <- matrice de confusion avec les étiquettes d'entrainement et les étiquettes S\n",
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"Calculer les métriques depuis M\n",
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"```\n",
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"\n",
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"- Validation croisée\n",
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"\n",
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"```\n",
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"K <- Valeurs à tester pour le nombre de voisins\n",
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"Pour un jeu d'entrainement x\n",
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"Permuter aléatoirement les nombre de 1 à N\n",
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"Diviser la permutation en L groupes approximativement égaux\n",
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"Pour l dans L:\n",
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" \n",
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"\n",
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"Pour k dans K:\n",
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" Pour l dans L:\n",
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" Effectuer l'entrainement avec k voisins, x[sans l] comme jeu d'entrainement \n",
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" Effectuer le test avec x[l] comme jeu de validation\n",
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" Calculer l'exactitude\n",
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" Prendre la moyenne des exactitudes\n",
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"Prendre le k avec la meilleur exactitude moyenne\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Iris Dataset"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On utilise 70% des données pour le jeu d'entrainement et 30% des données pour le jeu de test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"train1, train_labels1, test1, test_labels1 = ld.load_iris_dataset(train_ratio = 0.7)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On crée un premier modèle afin d'identifier la meilleure valeur de k"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/francois/gitea/ift7025-projet/Code/metrics.py:40: RuntimeWarning: invalid value encountered in double_scalars\n",
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" precision.append(cm[label_num,label_num] / sum(cm[:,label_num]))\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Le meilleur k est: 9\n"
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]
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}
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],
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"source": [
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"findbest_Knn = Knn.Knn()\n",
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"meilleur_k = findbest_Knn.set_best_k(train1, train_labels1, nb_split=5, k_potentiel=range(2,12))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On crée maintenant un nouveau modèle où on initialise la valeur de K avec celle trouvée précédemment"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"myKnn = Knn.Knn(meilleur_k)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On effectue l'entrainement du modèle (la copie du jeu d'entrainement et des étiquettes en mémoire) et on obtient les mesures de validation pour ce jeu d'entraînement. Les valeurs des métriques de précision et de rappel sont calculées pour chacune des étiquettes."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Matrice de confusion:\n",
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"[[35. 0. 0.]\n",
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" [ 0. 32. 1.]\n",
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" [ 0. 3. 34.]]\n",
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"\n",
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"Accuracy:\n",
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"0.9619047619047619\n",
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"\n",
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"Precision:\n",
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"[1.0, 0.9142857142857143, 0.9714285714285714]\n",
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"\n",
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"Recall\n",
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"[1.0, 0.9696969696969697, 0.918918918918919]\n"
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]
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}
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],
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"source": [
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"training_iris_knn = myKnn.train(train1, train_labels1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On effectue maintenant le test avec l'échantillon de test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Matrice de confusion:\n",
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"[[15. 0. 0.]\n",
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" [ 0. 16. 1.]\n",
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" [ 0. 1. 12.]]\n",
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"\n",
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"Accuracy:\n",
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"0.9555555555555556\n",
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"\n",
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"Precision:\n",
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"[1.0, 0.9411764705882353, 0.9230769230769231]\n",
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"\n",
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"Recall\n",
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"[1.0, 0.9411764705882353, 0.9230769230769231]\n"
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]
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}
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],
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"source": [
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"test_iris_knn = myKnn.test(test1, test_labels1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Monks Dataset"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"train2, train_labels2, test2, test_labels2 = ld.load_monks_dataset(1)\n",
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"train3, train_labels3, test3, test_labels3 = ld.load_monks_dataset(2)\n",
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"train4, train_labels4, test4, test_labels4 = ld.load_monks_dataset(3)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Premier sous-ensemble"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- On identifie la meilleure valeur de k"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Le meilleur k est: 4\n"
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]
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}
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],
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"source": [
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"findbest_Knn = Knn.Knn()\n",
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"meilleur_k = findbest_Knn.set_best_k(train2, train_labels2, nb_split=5, k_potentiel=range(2,12))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"myKnn2 = Knn.Knn(meilleur_k)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- On effectue l'entrainement du modèle"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Matrice de confusion:\n",
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"[[32. 30.]\n",
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" [16. 46.]]\n",
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"\n",
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"Accuracy:\n",
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"0.6290322580645161\n",
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"\n",
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"Precision:\n",
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"[0.6666666666666666, 0.6052631578947368]\n",
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"\n",
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"Recall\n",
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"[0.5161290322580645, 0.7419354838709677]\n"
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]
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}
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],
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"source": [
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"training_monks1_knn = myKnn2.train(train2, train_labels2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- On effectue maintenant le test avec l'échantillon de test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Matrice de confusion:\n",
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"[[129. 87.]\n",
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" [ 38. 178.]]\n",
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"\n",
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"Accuracy:\n",
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"0.7106481481481481\n",
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"\n",
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"Precision:\n",
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"[0.7724550898203593, 0.6716981132075471]\n",
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"\n",
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"Recall\n",
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"[0.5972222222222222, 0.8240740740740741]\n"
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]
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}
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],
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"source": [
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"test_monks1_knn = myKnn2.test(test2, test_labels2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Second sous-ensemble"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"- On identifie la meilleure valeur de k"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
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"Le meilleur k est: 5\n"
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]
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}
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],
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"source": [
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"findbest_Knn = Knn.Knn()\n",
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"meilleur_k = findbest_Knn.set_best_k(train3, train_labels3, nb_split=5, k_potentiel=range(2,12))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"myKnn3 = Knn.Knn(meilleur_k)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- On effectue l'entrainement du modèle"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
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"Matrice de confusion:\n",
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"[[104. 1.]\n",
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" [ 63. 1.]]\n",
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"\n",
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"Accuracy:\n",
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"0.621301775147929\n",
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"\n",
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"Precision:\n",
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"[0.6227544910179641, 0.5]\n",
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"\n",
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"Recall\n",
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"[0.9904761904761905, 0.015625]\n"
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]
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}
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],
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"source": [
|
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"training_monks2_knn = myKnn3.train(train3, train_labels3)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"- On effectue maintenant le test avec l'échantillon de test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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||
"outputs": [
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||
{
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||
"name": "stdout",
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||
"output_type": "stream",
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||
"text": [
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"Matrice de confusion:\n",
|
||
"[[286. 4.]\n",
|
||
" [133. 9.]]\n",
|
||
"\n",
|
||
"Accuracy:\n",
|
||
"0.6828703703703703\n",
|
||
"\n",
|
||
"Precision:\n",
|
||
"[0.6825775656324582, 0.6923076923076923]\n",
|
||
"\n",
|
||
"Recall\n",
|
||
"[0.9862068965517241, 0.06338028169014084]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"test_monks2_knn = myKnn3.test(test3, test_labels3)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Troisième sous-ensemble"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On identifie la meilleure valeur de k"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Le meilleur k est: 5\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"findbest_Knn = Knn.Knn()\n",
|
||
"meilleur_k = findbest_Knn.set_best_k(train4, train_labels4, nb_split=5, k_potentiel=range(2,12))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"myKnn4 = Knn.Knn(meilleur_k)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On effectue l'entrainement du modèle"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Matrice de confusion:\n",
|
||
"[[27. 35.]\n",
|
||
" [ 1. 59.]]\n",
|
||
"\n",
|
||
"Accuracy:\n",
|
||
"0.7049180327868853\n",
|
||
"\n",
|
||
"Precision:\n",
|
||
"[0.9642857142857143, 0.6276595744680851]\n",
|
||
"\n",
|
||
"Recall\n",
|
||
"[0.43548387096774194, 0.9833333333333333]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"training_monks3_knn = myKnn4.train(train4, train_labels4)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On effectue maintenant le test avec l'échantillon de test"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Matrice de confusion:\n",
|
||
"[[ 99. 105.]\n",
|
||
" [ 8. 220.]]\n",
|
||
"\n",
|
||
"Accuracy:\n",
|
||
"0.7384259259259259\n",
|
||
"\n",
|
||
"Precision:\n",
|
||
"[0.9252336448598131, 0.676923076923077]\n",
|
||
"\n",
|
||
"Recall\n",
|
||
"[0.4852941176470588, 0.9649122807017544]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"test_monks3_knn = myKnn4.test(test4, test_labels4)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Congressional Voting Records Dataset"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"train5, train_labels5, test5, test_labels5 = ld.load_congressional_dataset(0.7)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On identifie la meilleure valeur de k"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Le meilleur k est: 9\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"findbest_Knn = Knn.Knn()\n",
|
||
"meilleur_k = findbest_Knn.set_best_k(train5, train_labels5, nb_split=5, k_potentiel=range(2,12))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"myKnn5 = Knn.Knn(meilleur_k)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On effectue l'entrainement du modèle"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Matrice de confusion:\n",
|
||
"[[ 76. 33.]\n",
|
||
" [ 15. 180.]]\n",
|
||
"\n",
|
||
"Accuracy:\n",
|
||
"0.8421052631578947\n",
|
||
"\n",
|
||
"Precision:\n",
|
||
"[0.8351648351648352, 0.8450704225352113]\n",
|
||
"\n",
|
||
"Recall\n",
|
||
"[0.6972477064220184, 0.9230769230769231]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"training_congres_knn = myKnn5.train(train5, train_labels5)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"- On effectue maintenant le test avec l'échantillon de test"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Matrice de confusion:\n",
|
||
"[[42. 17.]\n",
|
||
" [ 6. 66.]]\n",
|
||
"\n",
|
||
"Accuracy:\n",
|
||
"0.8244274809160306\n",
|
||
"\n",
|
||
"Precision:\n",
|
||
"[0.875, 0.7951807228915663]\n",
|
||
"\n",
|
||
"Recall\n",
|
||
"[0.711864406779661, 0.9166666666666666]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"test_congres_knn = myKnn5.test(test5, test_labels5)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Algorithme Naive Bayes"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"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": "3.7.1"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|