{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### \n", "author: Aurélien Garivier\n", "\n", "# Dimension reduction for the MNIST dataset\n", "\n", "\n", "The Mnist dataset provides a (somewhat old but) very classical example of Machine Learning. The goal is simple and useful: recognize hand-written digits. This was an important challenge for the postal companies in the 1980s. \n", "\n", "It is available in sklearn (and on the webpage of Yann LeCun, a very famous researcher in Machine Learning in general and neural networks in particular). \n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "# loading a lot of facilities for numerical computations and graphs\n", "%pylab inline \n", "pylab.rcParams['figure.figsize'] = (20, 6) # to have larger plot\n", "seed(240979) #initialize random number generator\n", "\n", "# set working directory\n", "workingdir = './'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Loading the data set\n", "\n", "### 1.1 Description of the data set\n", "The MNIST data contains $n\\_tot=70000$ images of size $dimX\\times dimY=28\\times28$, and their *labels* (a digit between $0$ and $9$). \n", "The images are stored as lines of the matrix *mnist.data*. \n", "Each image can be reshaped as a matrix $im \\in \\mathcal{M}_{dimX, dimY}(\\mathbb{R})$, where $im[i,j]$ is the intensity level of pixel (i,j): 0 means 'white', 255 means 'black'.\n", "\n", "The labels, stored in *mnist.target*, are numbers (here, we cast them to integers) between $0$ and $9$. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loaded 70000 images of size 28x28\n", "Number of classes: 10\n", "Classes:\n", "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n" ] } ], "source": [ "# from sklearn.datasets import fetch_mldata # si besoin: sudo pip install -U scikit-learn ou (pour une install locale) pip install --user --install-option=\"--prefix=\" -U scikit-learn\n", "# mnist = fetch_mldata('MNIST original')#, data_home='./')\n", "# mnist.target = mnist.target.astype(int) # by default the digits are floating numbers: convert to integers\n", "\n", "from sklearn.datasets import fetch_openml\n", "X, y = fetch_openml('mnist_784', version=1, return_X_y=True)\n", "\n", "# defining general variables for use throuhout the notebook \n", "ntot, p = shape(mnist.data)\n", "dimX = int(sqrt(p))\n", "dimY = dimX \n", "nc = len(unique(y)) # number of classes\n", "\n", "print(\"Loaded %d images of size %dx%d\"%(n_tot, dimX, dimY))\n", "print(\"Number of classes: %d\"%(nc))\n", "print(\"Classes:\")\n", "print(sorted(unique(mnist.target)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 What does the data look like?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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