{ "metadata": { "name": "", "signature": "sha256:b3330e44a3387fdd4ba2174bb643c3671cabdedc0bf445d5d9c7389ee76fd4a0" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Aide au devoir 1" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext autoreload\n", "%autoreload 2\n", "%pylab inline\n", "%aimport numpy\n", "np=numpy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Charger les donn\u00e9es avec numpy" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Pour charger les donn\u00e9es, on doit sp\u00e9cifier le \"delimiter\", dans ce cas ci \",\"\n", "train_set = np.loadtxt(\"train_images.txt\", delimiter=\",\")\n", "train_labels = np.loadtxt(\"train_labels.txt\", delimiter=\",\")\n", "\n", "print \"X est de dimension\"\n", "print train_set.shape, \"\\n\"\n", "print \"Y est de dimension\"\n", "print train_labels.shape, \"\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "X est de dimension\n", "(1000, 784) \n", "\n", "Y est de dimension\n", "(1000, 10) \n", "\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Calculer efficacement le taux d'erreur de classification" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = train_set.shape[0]\n", "c = train_labels.shape[1]\n", "\n", "# Soit une matrice bidon qui repr\u00e9sente les pr\u00e9dictions d'un mod\u00e8le\n", "y_hat = np.random.multinomial(10, [1./float(c)]*c, size=N)\n", "\n", "# On prend l'indice maximal de chaque rang\u00e9e avec argmax(Y, axis=1)\n", "predictions = np.argmax(y_hat, axis=1)\n", "\n", "print \"Les 10 premi\u00e8res pr\u00e9dictions\"\n", "print predictions[:10], \"\\n\"\n", "\n", "# On fait de m\u00eame avec les classes encod\u00e9es sous forme one-hot\n", "classes = np.argmax(train_labels, axis=1)\n", "\n", "print \"Les 10 premi\u00e8res classes\"\n", "print classes[:10], \"\\n\"\n", "\n", "# On peut comparer tous les indices en m\u00eame temps grace \u00e0 numpy\n", "print \"Le r\u00e9sultat des 10 premi\u00e8res comparaisons\"\n", "print (classes != predictions)[:10], \"\\n\"\n", "\n", "# Il reste seulement \u00e0 calculer la moyenne. Chaque True est \u00e9valu\u00e9 \u00e0 1 et False \u00e0 0\n", "print \"La moyenne des comparaisons \u00e9valu\u00e9es \u00e0 True\"\n", "print (classes != predictions).mean(), \"\\n\"\n", "\n", "# Et voil\u00e0, reste plus qu'\u00e0 l'afficher sous forme de pourcentage\n", "print \"Le taux d'erreur de classification de notre mod\u00e8le bidon!\"\n", "print (classes != predictions).mean() * 100, \"%\", \"\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Les 10 premi\u00e8res pr\u00e9dictions\n", "[7 0 3 5 0 0 4 4 3 0] \n", "\n", "Les 10 premi\u00e8res classes\n", "[5 0 4 1 9 2 1 3 1 4] \n", "\n", "Le r\u00e9sultat des 10 premi\u00e8res comparaisons\n", "[ True False True True True True True True True True] \n", "\n", "La moyenne des comparaisons \u00e9valu\u00e9es \u00e0 True\n", "0.898 \n", "\n", "Le taux d'erreur de classification de notre mod\u00e8le bidon!\n", "89.8 % \n", "\n" ] } ], "prompt_number": 48 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Afficher des images avec matplotlib" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pour afficher une image au hasard dans l'ensemble\n", "random_idx = np.random.random_integers(N)\n", "pylab.imshow(train_set[random_idx].reshape((28,28)), cmap=\"gray\")\n", "pylab.show()\n", "\n", "# Pas besoin que \u00e7a soit une image \u00e0 la base, on peut aussi afficher une matrice bidon :) Comme... p(X|C_k) par exemple. :o\n", "matrice_bidon = np.random.normal(size=(28*28))\n", "pylab.imshow(matrice_bidon.reshape((28,28)), cmap=\"gray\")\n", "pylab.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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S18zSUfk5RSKwafGJwM7n1nuiyef06YUUl/MWUimSKttxcHCQhhM0DE7ZZUCk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