ufldl 深度学习入门 第三发： 自我学习与无监督特征学习
目的：使用稀疏自编码器提取特征，使用softmax做分类器，实现手写字符识别分类。
好处：相比较前面直接使用原始像素的softmax分类器（92%识别率），能够提升分类器的识别率，达到98%以上。
体会：通过自学习提取特征，能够模仿人类的大脑完成特征的抽象提取。而且是自动提取过程，对于海量数据，将有非常大的优势。
UFLDL学习链接：UFLDL，感谢吴恩达同学
说明：在实现这一节之前一定要先完成稀疏自编码器，softmax回归这两节，因为这一节的许多代码都是借用这两节的。
这里给出Andrew ng的代码以及自己的代码（YOUR CODE HERE 部分），并附上详细的说明分析
%% 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
beta = 3; % weight of sparsity penalty term
maxIter = 400; % 我的电脑内存在4G的情况下，设为400会内存溢出，于是我设为80
%% ======================================================================
% 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'); %这里得到784×60000 的matrix
mnistLabels = loadMNISTLabels('mnist/train-labels-idx1-ubyte'); % 这里得到 60000×1的matrix
% Set Unlabeled Set (All Images)
% Simulate a Labeled and Unlabeled set
labeledSet = find(mnistLabels >= 0 & mnistLabels <= 4); % 找到0-4数字的索引
unlabeledSet = find(mnistLabels >= 5); %找到5-9数字的索引，作为无标签数据，用来训练自编码器
numTrain = round(numel(labeledSet)/2); % 计算训练集的样本数量，取0-4中一般的样本作为
% softmax的训练样本，一半的样本作为测试样本
trainSet = labeledSet(1:numTrain); % 将0-4的数字分为两组，一半用来训练Softmax分类器
testSet = labeledSet(numTrain+1:end); %一半用来做测试集。
unlabeledData = mnistData(:, unlabeledSet); %得到无标签数据矩阵
trainData = mnistData(:, trainSet); % 得到有标签训练数据集矩阵
trainLabels = mnistLabels(trainSet)' + 1;
% Shift Labels to the Range 1-5，把原本的0-4的标签，变成了1-5的标签
testData = mnistData(:, testSet); %得到有标签测试数据集矩阵
testLabels = mnistLabels(testSet)' + 1;
% Shift Labels to the Range 1-5，把原本的0-4的标签，变成了1-5的标签
% 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;
% Use minFunc to minimize the function
addpath minFunc/
options.Method = 'lbfgs'; % Here, we use L-BFGS to optimize our cost
% function. Generally, for minFunc to work, you
% need a function pointer with two outputs: the
% function value and the gradient. In our problem,
% sparseAutoencoderCost.m satisfies this.
options.maxIter = maxIter; % Maximum number of iterations of L-BFGS to run
options.display = 'on';
% 调用minFunc，参数列表中传入sparseAutoencoderCost的函数句柄，
% 这样在函数minFunc中就可以调用该cost函数，从而不断迭代得到最优解
[opttheta, cost] = minFunc( @(p) sparseAutoencoderCost(p, ...
inputSize, hiddenSize, ...
lambda, sparsityParam, ...
beta, unlabeledData), ... % 这里传入unlabeledData，用作训练的数据集
theta, options);
%% -----------------------------------------------------
% Visualize weights
W1 = reshape(opttheta(1:hiddenSize * inputSize), hiddenSize, inputSize);
display_network(W1'); %？？？？为什么显示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.
% 把原始的特征转换成由稀疏自编码器提取的特征
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
numClasses=5;
lambda=1e-4;
options.maxIter = 100;
featureSize=hiddenSize;
% 注意这个size要改成提取出的feature的size，而不是原始的inputSize
softmaxModel = softmaxTrain(featureSize, numClasses, lambda, ...
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
% 我在使用minfunc迭代80次的情况下，
% 得到的识别率是 97.404890%
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%
%
% matlab中的使用函数
1 find（），可以返回矩阵a中满足条件的元素的索引值。
2 numel（a），返回矩阵a中的元素个数。
3 max（），上面代码中有一处用到[nop, pred] = max(theta * data); 这里max第一个返回值是参数矩阵每列的最大值，第二个返回值是参数矩阵每列最大值的行号。这里我们很方便的通过一个max函数，直接就得到了预测的结果，用的比较巧妙。