Deep Learning九之深度学习UFLDL教程：linear decoder_exercise（斯坦福大学深度学习教程）

%% CS294A/CS294W Linear Decoder Exercise

%  Instructions
%  ------------
% 
%  This file contains code that helps you get started on the
%  linear decoder exericse. For this exercise, you will only need to modify
%  the code in sparseAutoencoderLinearCost.m. You will not need to modify
%  any code in this file.

%%======================================================================
%% STEP 0: Initialization
%  Here we initialize some parameters used for the exercise.

imageChannels = 3;     % number of channels (rgb, so 3)

patchDim   = 8;          % patch dimension
numPatches = 100000;   % number of patches

visibleSize = patchDim * patchDim * imageChannels;  % number of input units 
outputSize  = visibleSize;   % number of output units
hiddenSize  = 400;           % number of hidden units 

sparsityParam = 0.035; % desired average activation of the hidden units.
lambda = 3e-3;         % weight decay parameter       
beta = 5;              % weight of sparsity penalty term       

epsilon = 0.1;           % epsilon for ZCA whitening

%%======================================================================
%% STEP 1: Create and modify sparseAutoencoderLinearCost.m to use a linear decoder,
%          and check gradients
%  You should copy sparseAutoencoderCost.m from your earlier exercise 
%  and rename it to sparseAutoencoderLinearCost.m. 
%  Then you need to rename the function from sparseAutoencoderCost to
%  sparseAutoencoderLinearCost, and modify it so that the sparse autoencoder
%  uses a linear decoder instead. Once that is done, you should check 
% your gradients to verify that they are correct.

% NOTE: Modify sparseAutoencoderCost first!

% To speed up gradient checking, we will use a reduced network and some
% dummy patches

debugHiddenSize = 5;
debugvisibleSize = 8;
patches = rand([8 10]);
theta = initializeParameters(debugHiddenSize, debugvisibleSize); 

[cost, grad] = sparseAutoencoderLinearCost(theta, debugvisibleSize, debugHiddenSize, ...
                                           lambda, sparsityParam, beta, ...
                                           patches);

% Check gradients
numGrad = computeNumericalGradient( @(x) sparseAutoencoderLinearCost(x, debugvisibleSize, debugHiddenSize, ...
                                                  lambda, sparsityParam, beta, ...
                                                  patches), theta);

% Use this to visually compare the gradients side by side
disp([numGrad grad]); 

diff = norm(numGrad-grad)/norm(numGrad+grad);
% Should be small. In our implementation, these values are usually less than 1e-9.
disp(diff); 

assert(diff < 1e-9, ‘Difference too large. Check your gradient computation again‘);

% NOTE: Once your gradients check out, you should run step 0 again to
%       reinitialize the parameters
%}

%%======================================================================
%% STEP 2: 从pathes中学习特征 Learn features on small patches
%  In this step, you will use your sparse autoencoder (which now uses a 
%  linear decoder) to learn features on small patches sampled from related
%  images.

%% STEP 2a: 加载数据 Load patches
%  In this step, we load 100k patches sampled from the STL10 dataset and
%  visualize them. Note that these patches have been scaled to [0,1]

load stlSampledPatches.mat  %怎么就就这个变量加到pathes上了呢？因为它里面自己定义了变量patches的值！
figure;
displayColorNetwork(patches(:, 1:100)); 

%% STEP 2b: 预处理 Apply preprocessing
%  In this sub-step, we preprocess the sampled patches, in particular, 
%  ZCA whitening them. 
% 
%  In a later exercise on convolution and pooling, you will need to replicate 
%  exactly the preprocessing steps you apply to these patches before 
%  using the autoencoder to learn features on them. Hence, we will save the
%  ZCA whitening and mean image matrices together with the learned features
%  later on.

% Subtract mean patch (hence zeroing the mean of the patches)
meanPatch = mean(patches, 2);  %为什么是对每行求平均，以前是对每列即每个样本求平均呀？因为以前是灰度图，现在是彩色图，如果现在对每列平均就是对三个通道求平均，这肯定不行
patches = bsxfun(@minus, patches, meanPatch);

% Apply ZCA whitening
sigma = patches * patches‘ / numPatches; %协方差矩阵
[u, s, v] = svd(sigma);
ZCAWhite = u * diag(1 ./ sqrt(diag(s) + epsilon)) * u‘;
patches = ZCAWhite * patches;

figure;
displayColorNetwork(patches(:, 1:100));

%% STEP 2c: Learn features
%  You will now use your sparse autoencoder (with linear decoder) to learn
%  features on the preprocessed patches. This should take around 45 minutes.

theta = initializeParameters(hiddenSize, visibleSize);

% Use minFunc to minimize the function
addpath minFunc/

options = struct;
options.Method = ‘lbfgs‘; 
options.maxIter = 400;
options.display = ‘on‘;

[optTheta, cost] = minFunc( @(p) sparseAutoencoderLinearCost(p, ...
                                   visibleSize, hiddenSize, ...
                                   lambda, sparsityParam, ...
                                   beta, patches), ...
                              theta, options);

% Save the learned features and the preprocessing matrices for use in 
% the later exercise on convolution and pooling
fprintf(‘Saving learned features and preprocessing matrices...\n‘);                          
save(‘STL10Features.mat‘, ‘optTheta‘, ‘ZCAWhite‘, ‘meanPatch‘);
fprintf(‘Saved\n‘);

%% STEP 2d: Visualize learned features

W = reshape(optTheta(1:visibleSize * hiddenSize), hiddenSize, visibleSize);
b = optTheta(2*hiddenSize*visibleSize+1:2*hiddenSize*visibleSize+hiddenSize);
figure;
displayColorNetwork( (W*ZCAWhite)‘);

function [cost,grad,features] = sparseAutoencoderLinearCost(theta, visibleSize, hiddenSize, ...
                                                            lambda, sparsityParam, beta, data)
%计算线性解码器代价函数及其梯度
% visibleSize:输入层神经单元节点数   
% hiddenSize:隐藏层神经单元节点数  
% lambda: 权重衰减系数 
% sparsityParam: 稀疏性参数
% beta: 稀疏惩罚项的权重 
% data: 训练集 
% theta：参数向量，包含W1、W2、b1、b2
% -------------------- YOUR CODE HERE --------------------
% Instructions:
%   Copy sparseAutoencoderCost in sparseAutoencoderCost.m from your
%   earlier exercise onto this file, renaming the function to
%   sparseAutoencoderLinearCost, and changing the autoencoder to use a
%   linear decoder.
% -------------------- YOUR CODE HERE --------------------                                    
% The input theta is a vector because minFunc only deal with vectors. In
% this step, we will convert theta to matrix format such that they follow
% the notation in the lecture notes.
W1 = reshape(theta(1:hiddenSize*visibleSize), hiddenSize, visibleSize);
W2 = reshape(theta(hiddenSize*visibleSize+1:2*hiddenSize*visibleSize), visibleSize, hiddenSize);
b1 = theta(2*hiddenSize*visibleSize+1:2*hiddenSize*visibleSize+hiddenSize);
b2 = theta(2*hiddenSize*visibleSize+hiddenSize+1:end);

% Loss and gradient variables (your code needs to compute these values)
m = size(data, 2); % 样本数量

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute the loss for the Sparse Autoencoder and gradients
%                W1grad, W2grad, b1grad, b2grad
%
%  Hint: 1) data(:,i) is the i-th example
%        2) your computation of loss and gradients should match the size
%        above for loss, W1grad, W2grad, b1grad, b2grad

% z2 = W1 * x + b1
% a2 = f(z2)
% z3 = W2 * a2 + b2
% h_Wb = a3 = f(z3)

z2 = W1 * data + repmat(b1, [1, m]);
a2 = sigmoid(z2);
z3 = W2 * a2 + repmat(b2, [1, m]);
a3 = z3;

rhohats = mean(a2,2);
rho = sparsityParam;
KLsum = sum(rho * log(rho ./ rhohats) + (1-rho) * log((1-rho) ./ (1-rhohats)));


squares = (a3 - data).^2;
squared_err_J = (1/2) * (1/m) * sum(squares(:));              %均方差项
weight_decay_J = (lambda/2) * (sum(W1(:).^2) + sum(W2(:).^2));%权重衰减项
sparsity_J = beta * KLsum;                                    %惩罚项

cost = squared_err_J + weight_decay_J + sparsity_J;%损失函数值

% delta3 = -(data - a3) .* fprime(z3);
% but fprime(z3) = a3 * (1-a3)
delta3 = -(data - a3);
beta_term = beta * (- rho ./ rhohats + (1-rho) ./ (1-rhohats));
delta2 = ((W2‘ * delta3) + repmat(beta_term, [1,m]) ) .* a2 .* (1-a2);

W2grad = (1/m) * delta3 * a2‘ + lambda * W2;   % W2梯度
b2grad = (1/m) * sum(delta3, 2);               % b2梯度
W1grad = (1/m) * delta2 * data‘ + lambda * W1; % W1梯度
b1grad = (1/m) * sum(delta2, 2);               % b1梯度

%-------------------------------------------------------------------
% Convert weights and bias gradients to a compressed form
% This step will concatenate and flatten all your gradients to a vector
% which can be used in the optimization method.
grad = [W1grad(:) ; W2grad(:) ; b1grad(:) ; b2grad(:)];

end
%-------------------------------------------------------------------
% We are giving you the sigmoid function, you may find this function
% useful in your computation of the loss and the gradients.
function sigm = sigmoid(x)

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

function displayColorNetwork(A)

% display receptive field(s) or basis vector(s) for image patches
%
% A         the basis, with patches as column vectors

% In case the midpoint is not set at 0, we shift it dynamically
if min(A(:)) >= 0
    A = A - mean(A(:)); % 0均值化
end

cols = round(sqrt(size(A, 2)));% 每行大图像中小图像块的个数

channel_size = size(A,1) / 3;
dim = sqrt(channel_size);   % 小图像块内每行或列像素点个数
dimp = dim+1;
rows = ceil(size(A,2)/cols);   % 每列大图像中小图像块的个数
B = A(1:channel_size,:);                   % R通道像素值
C = A(channel_size+1:channel_size*2,:);    % G通道像素值
D = A(2*channel_size+1:channel_size*3,:);  % B通道像素值
B=B./(ones(size(B,1),1)*max(abs(B)));% 归一化
C=C./(ones(size(C,1),1)*max(abs(C)));
D=D./(ones(size(D,1),1)*max(abs(D)));
% Initialization of the image
I = ones(dim*rows+rows-1,dim*cols+cols-1,3);

%Transfer features to this image matrix
for i=0:rows-1
  for j=0:cols-1
      
    if i*cols+j+1 > size(B, 2)
        break
    end
    
    % This sets the patch
    I(i*dimp+1:i*dimp+dim,j*dimp+1:j*dimp+dim,1) = ...
         reshape(B(:,i*cols+j+1),[dim dim]);
    I(i*dimp+1:i*dimp+dim,j*dimp+1:j*dimp+dim,2) = ...
         reshape(C(:,i*cols+j+1),[dim dim]);
    I(i*dimp+1:i*dimp+dim,j*dimp+1:j*dimp+dim,3) = ...
         reshape(D(:,i*cols+j+1),[dim dim]);

  end
end

I = I + 1; % 使I的范围从[-1,1]变为[0，2]
I = I / 2; % 使I的范围从[0，2]变为[0, 1]
imagesc(I); 
axis equal  % 等比坐标轴：设置屏幕高宽比，使得每个坐标轴的具有均匀的刻度间隔
axis off    % 关闭所有的坐标轴标签、刻度、背景

end