408 lines
83 KiB
Text
408 lines
83 KiB
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{
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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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"- Projet final présenté par: **François Pelletier**\n",
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"- Matricule: **908144032**\n",
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"- Dans le cadre du cours: **IFT-7025**\n",
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"\n",
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"# Librairies utilisées"
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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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"import numpy as np\n",
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"import load_datasets as ld\n",
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"import matplotlib.pyplot as plt\n",
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"import NeuralNet"
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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\n",
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"\n",
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"La présentation des résultats liés à ce jeu de données servira aussi à expliquer les concepts et répondre aux questions. Pour les autres jeux de données, seul les résultats et la discussion seront détaillés.\n",
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"\n",
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"- Chargement du jeu de données"
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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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"### Choix du nombre de neurones dans la couche cachée\n",
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"\n",
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"On doit identifier le nombre optimal de neurones dans la couche cachée dans l'intervalle $[4,50]$ pour chacun des 5 jeux de données. On itère sur chacun des jeux de validation croisée, pour chaque dimension et on calcule l'accuracy moyenne. La dimension qui a la meilleure accuracy moyenne est choisie pour construire le réseau de neurones."
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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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"source": [
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"choix_n_neurones = range(4,51)"
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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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"- Pour faire la séparation du jeu de données en $k_{cv}=5$ jeux de validation croisée, on génère une permutation sur les indices du jeu d'entrainement, puis, on sépare cet ensemble en 5 groupes."
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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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"k_cv = 5\n",
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"all_indices = range(len(train_labels1))\n",
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"np.random.seed(12345)\n",
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"indices_cv_test = np.sort(np.array_split(np.random.permutation(all_indices),k_cv))"
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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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"data": {
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"text/plain": [
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"array([[ 4, 9, 13, 19, 20, 25, 33, 37, 39, 40, 44, 47, 48,\n",
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" 54, 58, 62, 72, 76, 78, 87, 89],\n",
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" [ 2, 6, 8, 26, 28, 30, 35, 42, 45, 50, 51, 52, 57,\n",
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" 60, 63, 69, 74, 79, 90, 92, 96],\n",
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" [ 0, 16, 17, 18, 21, 22, 24, 27, 32, 46, 49, 65, 66,\n",
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" 68, 75, 83, 84, 85, 86, 88, 99],\n",
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" [ 3, 5, 12, 15, 23, 31, 43, 53, 55, 56, 61, 64, 67,\n",
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" 70, 71, 93, 94, 95, 97, 100, 104],\n",
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" [ 1, 7, 10, 11, 14, 29, 34, 36, 38, 41, 59, 73, 77,\n",
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" 80, 81, 82, 91, 98, 101, 102, 103]])"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"indices_cv_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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"source": [
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"indices_cv_train = [np.setdiff1d(all_indices,indices_cv_test[i]) for i in range(k_cv)]"
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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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"Ce jeux de données a trois classes possibles comme variable de sortie. On utilisera donc un réseau de neurones avec 3 neurones dans la couche de sortie, une pour chacune des valeurs possibles. Les valeurs de sortie du jeu de données sont transformées à l'aide d'un encodage binaire où la valeur de sortie est convertie en rang dans un vecteur (on commence à 0), prenant la valeur 1. Par exemple, la valeur 2 devient $[0,0,1]$."
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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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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/francois/ift7025-projet/Code/metrics.py:40: RuntimeWarning: invalid value encountered in double_scalars\n",
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" myPrecision = 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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"source": [
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"accuracy_cum = []\n",
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"for n_neurones in choix_n_neurones:\n",
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" accuracy_cv=[]\n",
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" for cv_set in range(k_cv):\n",
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" nn1 = NeuralNet.NeuralNet(np.array([4,n_neurones,3]),range(3))\n",
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" nn1.train(train1[indices_cv_train[cv_set]], train_labels1[indices_cv_train[cv_set]], 0.1, 1, verbose=False)\n",
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" _,accuracy,_,_,_ = nn1.test(train1[indices_cv_test[cv_set]], train_labels1[indices_cv_test[cv_set]], verbose=False)\n",
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" accuracy_cv.append(accuracy)\n",
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" accuracy_cum.append(np.mean(np.array(accuracy_cv)))"
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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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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x7f054f634ac8>]"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"plt.plot(choix_n_neurones,accuracy_cum)"
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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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"Le nombre de neurones qui maximise l'accuracy est de:"
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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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{
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"data": {
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"text/plain": [
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"49"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"n_neurones_optimal1 = choix_n_neurones[np.where(accuracy_cum==max(accuracy_cum))[0][0]]\n",
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"n_neurones_optimal1"
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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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"### Choix du nombre de couches cachées\n",
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"\n",
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"On choisit un nombre de 1 à 5 couches cachées. Le nombre de couche ayany l'accuracy maximale sera sélectionné pour la construction du réseau. On effectue 10 époques étant donné la taille des réseaux à entrainer."
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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": 27,
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"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"choix_n_couches = range(1,6)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 21,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"accuracy_cum = []\n",
|
||
|
|
"lc_cum = []\n",
|
||
|
|
"for n_couches in choix_n_couches:\n",
|
||
|
|
" accuracy_cv=[]\n",
|
||
|
|
" nn1 = NeuralNet.NeuralNet(np.hstack((4,np.repeat(n_neurones_optimal1,n_couches),3)),range(3))\n",
|
||
|
|
" lc = nn1.train(train1, train_labels1, 0.1, 10, verbose=False)\n",
|
||
|
|
" lc_cum.append(lc)\n",
|
||
|
|
" _,accuracy,_,_,_ = nn1.test(train1, train_labels1, verbose=False)\n",
|
||
|
|
" accuracy_cv.append(accuracy)\n",
|
||
|
|
" accuracy_cum.append(np.mean(np.array(accuracy_cv)))\n",
|
||
|
|
"lc_cum = np.array(lc_cum)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[<matplotlib.lines.Line2D at 0x7f054f4e1588>]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(choix_n_couches,accuracy_cum)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Le nombre de couches cachées qui maximise l'accurary est de:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 32,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"4"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 32,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"n_couches_optimal1 = choix_n_couches[np.where(accuracy_cum==max(accuracy_cum))[0][0]]\n",
|
||
|
|
"n_couches_optimal1"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Courbes d'apprentissage\n",
|
||
|
|
"\n",
|
||
|
|
"Ce graphique présente les courbes d'apprentissage pour chacun des niveaux de profondeur du réseau"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 31,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.subplot(111)\n",
|
||
|
|
"for i in choix_n_couches:\n",
|
||
|
|
" plt.plot(range(10),lc_cum[i-1], label=\"%d couches\"%(i,))\n",
|
||
|
|
"leg = plt.legend(loc='best', ncol=2, mode=\"expand\", shadow=True, fancybox=True)\n",
|
||
|
|
"leg.get_frame().set_alpha(0.5)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Choix des poids initiaux\n",
|
||
|
|
"Les poids initiaux ont été choisis à partir d'une distribution uniforme sur $[-1,1]$. On compare ici les courbes d'apprentissage en initialisant les poids à 0 et en initialisant les poids aléatoirement, pour le réseau de dimension et de profondeur optimale sélectionnées précédemment."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Entrainement et tests\n",
|
||
|
|
"On reprend les résultats du dernier entrainement, puisqu'il utilise les poids aléatoires et les hyperparamètres optimaux."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"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": "3.7.3"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 2
|
||
|
|
}
|