UFLDL教程（六）之栈式自编码器

素颜马尾好姑娘i 2021-07-16 23:43 431阅读 0赞

**第** **0** **步：初始化一些参数和常数**

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**第****1****步：利用训练样本集训练第一个稀疏编码器**

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**第****2****步：利用训练样本集训练第二个稀疏编码器**

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**第****3****步：利用第二个稀疏编码器提取到的特征训练****softmax****回归模型**

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**第****4****步：利用误差反向传播进行微调**

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**第****5****步：利用测试样本集对得到的分类器进行精度测试**

**下面将程序实现过程中的关键代码post出，欢迎各位网友指点！**

**stackedAEExercise.m**

clc
    clear
    close all
    
    addpath ../common/
    addpath ../common/minFunc
    
    %%======================================================================
    %% STEP 0: 设置多层自编码器的相关参数
    % 整个网络的输入输出结构
    inputSize = 28 * 28; 
    numClasses = 10;
    % 稀疏自编码器结构
    hiddenSizeL1 = 200;    % Layer 1 Hidden Size
    hiddenSizeL2 = 200;    % Layer 2 Hidden Size
    % 一些权值
    sparsityParam = 0.1;    % desired average activation of the hidden units.that is ρ in the lecture
    beta = 3;                    % weight of sparsity penalty term       
    lambda = 3e-3;           % weight decay parameter       
    
    
    %%======================================================================
    %% STEP 1: 载入MNSIT数据集及标签集
    addpath mnist\
    trainData = loadMNISTImages('mnist/train-images-idx3-ubyte');
    trainLabels = loadMNISTLabels('mnist/train-labels-idx1-ubyte');
    trainLabels(trainLabels == 0) = 10; % Remap 0 to 10 since our labels need to start from 1
    
    
    %%======================================================================
    %% STEP 2: 训练第一个稀疏自编码器（训练样本集为trainData，看作是无标签训练样本集）
    
    %  Randomly initialize the parameters
    sae1Theta = initializeParameters(hiddenSizeL1, inputSize);
    
    %  利用无标签样本集对稀疏自编码器进行学习，学习到的参数存放在向量sae1OptTheta中
    % 优化函数的一些参数设置
    options.Method = 'lbfgs'; 
    options.maxIter = 400;      % Maximum number of iterations of L-BFGS to run 
    options.display = 'on';
    % 调用优化函数，得到优化向量sae1OptTheta
    
    [sae1OptTheta, ~] = minFunc( @(p) sparseAutoencoderCost(p, ...
                                       inputSize, hiddenSizeL1, ...    %输入维数、输出维数
                                       lambda, sparsityParam, ...
                                       beta, trainData), ...
                                  sae1Theta, options);
    %save('sae1OptTheta.mat','sae1OptTheta')
    % % 权值可视化（Visualize weights）
    % W11 = reshape(sae1OptTheta(1:hiddenSizeL1 * inputSize), hiddenSizeL1, inputSize);
    % display_network(W11');
    % load('sae1OptTheta.mat');
    
    %%======================================================================
    %% STEP 3: 训练第二个稀疏自编码器（训练数据是第一个自编码器提取到的特征）
    
    % 求解第一个自编码器的输出sae1Features（维数为hiddenSizeL1）
    [sae1Features] = feedForwardAutoencoder(sae1OptTheta, hiddenSizeL1, ...
                                            inputSize, trainData);
    
    %  Randomly initialize the parameters
    sae2Theta = initializeParameters(hiddenSizeL2, hiddenSizeL1);
    
    % 开始训练第二个自编码器，输入维数是hiddenSizeL1，输出维数是hiddenSizeL2，优化向量存放在sae2OptTheta中
    [sae2OptTheta, ~] = minFunc( @(p) sparseAutoencoderCost(p, ...
                                       hiddenSizeL1, hiddenSizeL2, ... %输入维数、输出维数
                                       lambda, sparsityParam, ...
                                       beta, sae1Features), ...
                                  sae2Theta, options);                        
    % save('sae2OptTheta.mat','sae2OptTheta')  
    % % Visualize weights 
    % % W21 = reshape(sae2OptTheta(1:hiddenSizeL2 * hiddenSizeL1), hiddenSizeL2, hiddenSizeL1);
    % % display_network(W21'); %无法可视化！！
    % load('sae2OptTheta.mat');
    %%======================================================================
    %% STEP 4: 训练softmax classifier（它的输入为第二个自编码器提取到的特征sae2Features）
    
    % 求解第二个自编码器的输出sae1Features（维数为hiddenSizeL2）
    [sae2Features] = feedForwardAutoencoder(sae2OptTheta, hiddenSizeL2, ...
                                            hiddenSizeL1, sae1Features);
    
    %  Randomly initialize the parameters
    saeSoftmaxTheta = 0.005 * randn(hiddenSizeL2 * numClasses, 1);
    
    % 开始优化softmax classifier，得到优化向量
    options.maxIter = 100;
    softmaxModel = softmaxTrain(size(sae2Features,1), numClasses, lambda, ...
                                sae2Features, trainLabels, options);
    saeSoftmaxOptTheta=softmaxModel.optTheta(:);
    % load('saeSoftmaxOptTheta.mat')
    
    %%======================================================================
    %% STEP 5: 微调多层自编码器
    
    % 利用稀疏自编码(stack)和softmax分类器(saeSoftmaxOptTheta)学习到的参数作为微调模型的初始值
    % 稀疏自编码的参数stack
    stack = cell(2,1);%存放稀疏自编码器参数的元胞
    stack{
        1}.w = reshape(sae1OptTheta(1:hiddenSizeL1*inputSize), ...
                         hiddenSizeL1, inputSize);
    stack{
        1}.b = sae1OptTheta(2*hiddenSizeL1*inputSize+1:2*hiddenSizeL1*inputSize+hiddenSizeL1);
    stack{
        2}.w = reshape(sae2OptTheta(1:hiddenSizeL2*hiddenSizeL1), ...
                         hiddenSizeL2, hiddenSizeL1);
    stack{
        2}.b = sae2OptTheta(2*hiddenSizeL2*hiddenSizeL1+1:2*hiddenSizeL2*hiddenSizeL1+hiddenSizeL2);
    [stackparams, netconfig] = stack2params(stack);%所有stack转化为向量形式，并提取稀疏自编码器的结构
    % 整个模型参数（saeSoftmaxOptTheta+stack）
    stackedAETheta = [ saeSoftmaxOptTheta ; stackparams ];
    
    % 是否进行梯度检验    
    DEBUG=1;                                      
    if DEBUG
        checkStackedAECost()      
    end      
    
    % 开始进行微调优化 （Use minFunc to minimize the function）
    [stackedAEOptTheta, cost] = minFunc( @(p) stackedAECost(p, ...
                                           inputSize, hiddenSizeL2,...%输入层维数、最后一个稀疏编码器隐藏层维数
                                           numClasses, netconfig, ...%稀疏自编码器的结构
                                           lambda, trainData, trainLabels), ...
                                           stackedAETheta, options); 
                                       
    %%======================================================================
    %% STEP 6: Test 
    % 获取有标签样本集
    testData = loadMNISTImages('mnist/t10k-images-idx3-ubyte');
    testLabels = loadMNISTLabels('mnist/t10k-labels-idx1-ubyte');
    testLabels(testLabels == 0) = 10; % Remap 0 to 10
    
    % 进行预测（微调后的）
    [pred] = stackedAEPredict(stackedAEOptTheta, inputSize, hiddenSizeL2, ...
                              numClasses, netconfig, testData);
    acc = mean(testLabels(:) == pred(:));% 计算预测精度
    fprintf('After Finetuning Test Accuracy: %0.3f%%\n', acc * 100);
    
    % 进行预测（微调前的）
    [pred] = stackedAEPredict(stackedAETheta, inputSize, hiddenSizeL2, ...
                              numClasses, netconfig, testData);
    acc = mean(testLabels(:) == pred(:));% 计算预测精度
    fprintf('Before Finetuning Test Accuracy: %0.3f%%\n', acc * 100);
    
    % Accuracy is the proportion of correctly classified images
    % The results for our implementation were:
    
    % Before Finetuning Test Accuracy: 87.7%
    % After Finetuning Test Accuracy:  97.6%
    %
    % If your values are too low (accuracy less than 95%), you should check 
    % your code for errors, and make sure you are training on the 
    % entire data set of 60000 28x28 training images 
    % (unless you modified the loading code, this should be the case)

** stackedAEPredict.m**

% stackedAEPredict: Takes a trained theta and a test data set,
    % and returns the predicted labels for each example.
                                             
    % theta: trained weights from the autoencoder
    % visibleSize: the number of input units
    % hiddenSize:  the number of hidden units *at the 2nd layer*
    % numClasses:  the number of categories
    % data: Our matrix containing the training data as columns.  So, data(:,i) is the i-th training example. 
    
    % Your code should produce the prediction matrix 
    % pred, where pred(i) is argmax_c P(y(c) | x(i)).
     
    function [pred] = stackedAEPredict(theta, inputSize, hiddenSize, numClasses, netconfig, data)
                                             
    
    %% Unroll theta parameter
    
    % We first extract the part which compute the softmax gradient
    softmaxTheta = reshape(theta(1:hiddenSize*numClasses), numClasses, hiddenSize);
    
    % Extract out the "stack"
    stack = params2stack(theta(hiddenSize*numClasses+1:end), netconfig);
    
    %% ---------- YOUR CODE HERE --------------------------------------
    %  Instructions: Compute pred using theta assuming that the labels start from 1.
    
    %% 前向传播计算
    a{
        1}=data;
    depth=numel(netconfig.layersizes);
    for i=1:depth
        a{i+1}=sigmoid(bsxfun(@plus,stack{i}.w*a{i},stack{i}.b)); 
    end
    
    %% softmax模型的输出Htheta
    softmaxData=a{depth+1};%softmax的输入即为stack自编码器最后一层的输出
    M=softmaxTheta*softmaxData;%矩阵M
    M=bsxfun(@minus,M,max(M));%减去行向量α，防止数据溢出
    Htheta=bsxfun(@rdivide,exp(M),sum(exp(M)));%softmax模型的假设函数输出
    
    %% 计算Htheta每一列最大元素所在位置，即为该列所对应样本的类别
    [~,pred]=max(Htheta);
    
    
    
    end
    
    
    % You might find this useful
    function sigm = sigmoid(x)
        sigm = 1 ./ (1 + exp(-x));
    end

**stackedAECost.m**

%{
    Takes a trained softmaxTheta and a training data set with labels,
    and returns cost and gradient using a stacked autoencoder model. Used for finetuning.
    输入：
    theta：整个网络的权值向量
    visibleSize: 网络的输入层维数
    hiddenSize:  最后一个稀疏自编码器的隐藏层维数
    numClasses:  类别总数
    netconfig:   the network configuration of the stack
    lambda:      the weight regularization penalty
    data: 训练样本集，data(:,i) is the i-th training example. 
    labels: 训练样本集的标签, where labels(i) is the label for the i-th training example
    输出：
    cost：代价函数
    grad：梯度向量
    %}                                   
    
    function [ cost, grad ] = stackedAECost(theta, ...
                                                  inputSize, hiddenSize, ...%输入层维数、最后一个稀疏编码器隐藏层维数
                                                  numClasses, netconfig, ...%总类数、稀疏自编码器的结构
                                                  lambda, data, labels)     
                                              
    %% 从输入的网络参数向量theta中得到softmax分类器和稀疏自编码器的参数
    softmaxTheta = reshape(theta(1:hiddenSize*numClasses), numClasses, hiddenSize);%softmax的参数矩阵
    stack = params2stack(theta(hiddenSize*numClasses+1:end), netconfig);% Extract out the "stack"
    
    %% 初始化
    %样本个数
    numCases = size(data, 2); 
    %样本标签矩阵groundTruth（即I阵）
    groundTruth = full(sparse(labels, 1:numCases, 1));
    % softmax分类器的梯度
    softmaxThetaGrad = zeros(size(softmaxTheta));
    % 稀疏自编码器的梯度（权值w和偏执项b）
    stackgrad = cell(size(stack));
    for d = 1:numel(stack)
        stackgrad{d}.w = zeros(size(stack{d}.w));
        stackgrad{d}.b = zeros(size(stack{d}.b));
    end
    
    
    %% 前向传播算法
    % 初始化工作 
    depth=numel(stack);% 稀疏自编码器隐藏层的层数(the layor of the network)
    z=cell(depth+1,1); % stack网络各层的激励值
    a=cell(depth+1,1); % stack网络各层的激励值
    a{
        1}=data; % 输入层数据
    
    % 各稀疏自编码器输出a{
       2},...,a{depth+1}
    for i=1:depth
        %各稀疏编码器提取到的features 
        z{i+1}=bsxfun(@plus,stack{i}.w*a{i},stack{i}.b);
        a{i+1}=sigmoid(z{i+1});
    end
    
    % softmax分类器的输出Htheta
    softmaxData=a{depth+1};%softmax的输入即为stack自编码器最后一层的输出
    M=softmaxTheta*softmaxData;%矩阵M
    M=bsxfun(@minus,M,max(M));%减去行向量α，防止数据溢出
    Htheta=bsxfun(@rdivide,exp(M),sum(exp(M)));%softmax分类器的假设函数输出
    
    %% 多层网络代价函数的计算（%要对整个网络的所有参数，包括softmax分类器和自编码器的所有参数）
    cost=-sum(sum(groundTruth.*log(Htheta)))/numCases+lambda*sum(softmaxTheta(:).^2)/2;
    
    
    %% 梯度计算
    
    % softmax层的梯度
    softmaxThetaGrad=-(groundTruth-Htheta)*softmaxData'/numCases+lambda*softmaxTheta;
    
    %  稀疏自编码层
    %  敏感度
    delta=cell(depth+1,1);
    delta{depth+1}=-softmaxTheta'*(groundTruth-Htheta).*a{depth+1}.*(1-a{depth+1});
    for i=depth:-1:2
        delta{i}=stack{i}.w'*delta{i+1}.*(a{i}).*(1-a{i});  
    end
    % 梯度值
    for i=depth:-1:1
        stackgrad{i}.w=delta{i+1}*a{i}'/numCases;
        stackgrad{i}.b=sum(delta{i+1},2)'/numCases;
        if size(stackgrad{i}.b,2)~=1
            stackgrad{i}.b=stackgrad{i}.b';
        end
    end
    
    %% Roll gradient vector
    grad = [softmaxThetaGrad(:) ; stack2params(stackgrad)];
    
    end
    
    % You might find this useful
    function sigm = sigmoid(x)
        sigm = 1 ./ (1 + exp(-x));
    end