Deep Learning 学习随记（四）自学习和非监督特征学习

接着看讲义，接下来这章应该是Self-Taught Learning and Unsupervised Feature Learning。

含义：

从字面上不难理解其意思。这里的self-taught learning指的是用非监督的方法提取特征，然后用监督方法进行分类。比如用稀疏自编码+softmax regression。

对于非监督特征学习，有两种类型，一类是self-taught learning，一类是semi-supervised learning。看他们的定义不如看讲义中给出的那个简单的例子：

假定有一个计算机视觉方面的任务，目标是区分汽车和摩托车图像；也即训练样本里面要么是汽车的图像，要么是摩托车的图像。哪里获取大量的无类标数据呢？最简单的方式可能是到互联网上下载一些随机的图像数据集，这这些数据上训练出一个稀疏自编码神经网络，从中得到有用的特征。这个例子里，无类标数据完全来自于一个和带类标数据不同的分布（无类标数据集中，或许其中一些图像包含汽车或者摩托车，但是不是所有的图像都如此）。这种情形被称为自学习。

相反，如果有大量的无类标图像数据，要么是汽车图像，要么是摩托车图像，仅仅是缺失了类标（没有标注每张图片到底是汽车还是摩托车）。也可以用这些无类标数据来学习特征。这种方式，即要求无类标样本和带类标样本服从相同的分布，有时候被称为半监督学习。在实践中，常常无法找到满足这种要求的无类标数据（到哪里找到一个每张图像不是汽车就是摩托车，只是丢失了类标的图像数据库？）因此，自学习被广泛的应用于从无类标数据集中学习特征。

练习：

下面是讲义中的练习，要解决的还是MNIST手写库的识别问题，主要过程就是稀疏自编码提取特征然后用softmax regression分类。

一开始用一台32位的机器跑，出现内存不够的情况，后来换了台64位的机器才好。主要代码如下：

stlExercise.m:

%% 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;

%% ======================================================================
%  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;
%  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 = 400;      % Maximum number of iterations of L-BFGS to run
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
options.maxIter = 100;
softmax_lambda = 1e-4;
inputSize = 200;              %features的维度与data的维度不一样了
softmaxModel = softmaxTrain(inputSize, numLabels, softmax_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);
acc = mean(testLabels(:) == pred(:));
fprintf('Accuracy: %0.3f%%\n', acc * 100);

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

% 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.m:

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.
activation = W1*data+repmat(b1,[1,size(data,2)]);
activation = sigmoid(activation);

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

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

实验结果如下：

最终的正确率：

讲义和代码中提到正确率在98.3%，基本差不多。