机器学习课程练习（五）——自我学习

前言

斯坦福的UFLDL教程每一个章节都配有练习

本文是自我学习这一章节的练习的解答

练习的目的是通过组合稀疏自动编码机和softmax分类器，实现一个从手写体中自动提取特征并识别的识别器

具体内容可以浏览课程网页

注意

softmax的输入是自动编码器的输出，用“无标签”数据训练自动编码机后，用得到的参数处理softmax的训练集和测试集

stlExercise完整代码

%% CS294A/CS294W Self-taught Learning Exercise

%  Instructions
%  ------------
% 
%  This file contains code that helps you get started on the
%  self-taught learning. You will need to complete code in feedForwardAutoencoder.m
%  You will also need to have implemented sparseAutoencoderCost.m and 
%  softmaxCost.m from previous exercises.
%
%% ======================================================================
%  STEP 0: Here we provide the relevant parameters values that will
%  allow your sparse autoencoder to get good filters; you do not need to 
%  change the parameters below.

inputSize  = 28 * 28;
numLabels  = 5;
hiddenSize = 200;
sparsityParam = 0.1; % desired average activation of the hidden units.
                     % (This was denoted by the Greek alphabet rho, which looks like a lower-case "p",
		             %  in the lecture notes). 
lambda = 3e-3;       % weight decay parameter   
lambda_softmax = 1e-4;    
beta = 3;            % weight of sparsity penalty term   
maxIter = 400;

%% ======================================================================
%  STEP 1: Load data from the MNIST database
%
%  This loads our training and test data from the MNIST database files.
%  We have sorted the data for you in this so that you will not have to
%  change it.

% Load MNIST database files
mnistData   = loadMNISTImages('mnist/train-images-idx3-ubyte');
mnistLabels = loadMNISTLabels('mnist/train-labels-idx1-ubyte');

% Set Unlabeled Set (All Images)

% Simulate a Labeled and Unlabeled set
labeledSet   = find(mnistLabels >= 0 & mnistLabels <= 4);
unlabeledSet = find(mnistLabels >= 5);

numTrain = round(numel(labeledSet)/2);
trainSet = labeledSet(1:numTrain);
testSet  = labeledSet(numTrain+1:end);

unlabeledData = mnistData(:, unlabeledSet);

trainData   = mnistData(:, trainSet);
trainLabels = mnistLabels(trainSet)' + 1; % Shift Labels to the Range 1-5

testData   = mnistData(:, testSet);
testLabels = mnistLabels(testSet)' + 1;   % Shift Labels to the Range 1-5

% Output Some Statistics
fprintf('# examples in unlabeled set: %d\n', size(unlabeledData, 2));
fprintf('# examples in supervised training set: %d\n\n', size(trainData, 2));
fprintf('# examples in supervised testing set: %d\n\n', size(testData, 2));

%% ======================================================================
%  STEP 2: Train the sparse autoencoder
%  This trains the sparse autoencoder on the unlabeled training
%  images. 

%  Randomly initialize the parameters
theta = initializeParameters(hiddenSize, inputSize);

%% ----------------- YOUR CODE HERE ----------------------
%  Find opttheta by running the sparse autoencoder on
%  unlabeledTrainingImages

opttheta = theta; 
addpath minFunc/
options.Method = 'lbfgs';
options.maxIter = maxIter;
options.display = 'on';
[opttheta, cost] = minFunc( @(p) sparseAutoencoderCost(p, ...
                                   inputSize, hiddenSize, ...
                                   lambda, sparsityParam, ...
                                   beta, unlabeledData), ...
                              theta, options);

%% -----------------------------------------------------
                          
% Visualize weights
W1 = reshape(opttheta(1:hiddenSize * inputSize), hiddenSize, inputSize);
display_network(W1');

%%======================================================================
%% STEP 3: Extract Features from the Supervised Dataset
%  
%  You need to complete the code in feedForwardAutoencoder.m so that the 
%  following command will extract features from the data.

trainFeatures = feedForwardAutoencoder(opttheta, hiddenSize, inputSize, ...
                                       trainData);

testFeatures = feedForwardAutoencoder(opttheta, hiddenSize, inputSize, ...
                                       testData);

%%======================================================================
%% STEP 4: Train the softmax classifier

softmaxModel = struct;  
%% ----------------- YOUR CODE HERE ----------------------
%  Use softmaxTrain.m from the previous exercise to train a multi-class
%  classifier. 

%  Use lambda = 1e-4 for the weight regularization for softmax

% You need to compute softmaxModel using softmaxTrain on trainFeatures and
% trainLabels

softmaxModel = softmaxTrain(hiddenSize, numLabels, lambda_softmax, ...
                            trainFeatures, trainLabels, options);

%% -----------------------------------------------------

%%======================================================================
%% STEP 5: Testing 

%% ----------------- YOUR CODE HERE ----------------------
% Compute Predictions on the test set (testFeatures) using softmaxPredict
% and softmaxModel

[pred] = softmaxPredict(softmaxModel, testFeatures);

%% -----------------------------------------------------

% Classification Score
fprintf('Test Accuracy: %f%%\n', 100*mean(pred(:) == testLabels(:)));

% (note that we shift the labels by 1, so that digit 0 now corresponds to
%  label 1)
%
% Accuracy is the proportion of correctly classified images
% The results for our implementation was:
%
% Accuracy: 98.3%
%
% 

feedForwardAutoencoder代码

function [activation] = feedForwardAutoencoder(theta, hiddenSize, visibleSize, data)

% theta: trained weights from the autoencoder
% visibleSize: the number of input units (probably 64) 
% hiddenSize: the number of hidden units (probably 25) 
% data: Our matrix containing the training data as columns.  So, data(:,i) is the i-th training example. 
  
% We first convert theta to the (W1, W2, b1, b2) matrix/vector format, so that this 
% follows the notation convention of the lecture notes. 

W1 = reshape(theta(1:hiddenSize*visibleSize), hiddenSize, visibleSize);
b1 = theta(2*hiddenSize*visibleSize+1:2*hiddenSize*visibleSize+hiddenSize);

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute the activation of the hidden layer for the Sparse Autoencoder.
%训练数据个数
number_data = size(data,2);
%前向计算
activation = sigmoid(W1 * data + repmat(b1,1,number_data));

%-------------------------------------------------------------------

end

%-------------------------------------------------------------------
% Here's an implementation of the sigmoid function, which you may find useful
% in your computation of the costs and the gradients.  This inputs a (row or
% column) vector (say (z1, z2, z3)) and returns (f(z1), f(z2), f(z3)). 

function sigm = sigmoid(x)
    sigm = 1 ./ (1 + exp(-x));
end