Exercise:Sparse Autoencoder

function patches = sampleIMAGES()
% sampleIMAGES
% Returns 10000 patches for training

load IMAGES;    % load images from disk 

patchsize = 8;  % we‘ll use 8x8 patches 
numpatches = 10000;

% Initialize patches with zeros.  Your code will fill in this matrix--one
% column per patch, 10000 columns. 
patches = zeros(patchsize*patchsize, numpatches);

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Fill in the variable called "patches" using data 
%  from IMAGES.  
%  
%  IMAGES is a 3D array containing 10 images
%  For instance, IMAGES(:,:,6) is a 512x512 array containing the 6th image,
%  and you can type "imagesc(IMAGES(:,:,6)), colormap gray;" to visualize
%  it. (The contrast on these images look a bit off because they have
%  been preprocessed using using "whitening."  See the lecture notes for
%  more details.) As a second example, IMAGES(21:30,21:30,1) is an image
%  patch corresponding to the pixels in the block (21,21) to (30,30) of
%  Image 1


imageNum = randi([1,10]);     %随机的选择一张图片
[rowNum colNum] = size(IMAGES(:,:,imageNum));
xPos = randperm(rowNum-patchsize+1,100);
yPos = randperm(colNum-patchsize+1,100);
for ii = 1:100                %在图片中选取100*100个像素点
    for jj = 1:100
        patchNum = (ii-1)*100 + jj;
        patches(:,patchNum) = reshape(IMAGES(xPos(ii):xPos(ii)+7,yPos(jj):yPos(jj)+7,...
                                      imageNum),64,1);
    end
end



%% ---------------------------------------------------------------
% For the autoencoder to work well we need to normalize the data
% Specifically, since the output of the network is bounded between [0,1]
% (due to the sigmoid activation function), we have to make sure 
% the range of pixel values is also bounded between [0,1]
patches = normalizeData(patches);

end


%% ---------------------------------------------------------------
function patches = normalizeData(patches)

% Squash data to [0.1, 0.9] since we use sigmoid as the activation
% function in the output layer

% Remove DC (mean of images). 
patches = bsxfun(@minus, patches, mean(patches));

% Truncate to +/-3 standard deviations and scale to -1 to 1
pstd = 3 * std(patches(:));
patches = max(min(patches, pstd), -pstd) / pstd;

% Rescale from [-1,1] to [0.1,0.9]
patches = (patches + 1) * 0.4 + 0.1;

end

function [cost,grad] = sparseAutoencoderCost(theta, visibleSize, hiddenSize, ...
                                             lambda, sparsityParam, beta, data)

% visibleSize: the number of input units (probably 64) 
% hiddenSize: the number of hidden units (probably 25) 
% lambda: weight decay parameter
% sparsityParam: The desired average activation for the hidden units (denoted in the lecture
%                           notes by the greek alphabet rho, which looks like a lower-case "p").
% beta: weight of sparsity penalty term
% data: Our 64x10000 matrix containing the training data.  So, data(:,i) is the i-th training example. 
  
% The input theta is a vector (because minFunc expects the parameters to be a vector). 
% 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);
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);

% Cost and gradient variables (your code needs to compute these values). 
% Here, we initialize them to zeros. 
cost = 0;
W1grad = zeros(size(W1)); 
W2grad = zeros(size(W2));
b1grad = zeros(size(b1)); 
b2grad = zeros(size(b2));

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute the cost/optimization objective J_sparse(W,b) for the Sparse Autoencoder,
%                and the corresponding gradients W1grad, W2grad, b1grad, b2grad.
%
% W1grad, W2grad, b1grad and b2grad should be computed using backpropagation.
% Note that W1grad has the same dimensions as W1, b1grad has the same dimensions
% as b1, etc.  Your code should set W1grad to be the partial derivative of J_sparse(W,b) with
% respect to W1.  I.e., W1grad(i,j) should be the partial derivative of J_sparse(W,b) 
% with respect to the input parameter W1(i,j).  Thus, W1grad should be equal to the term 
% [(1/m) \Delta W^{(1)} + \lambda W^{(1)}] in the last block of pseudo-code in Section 2.2 
% of the lecture notes (and similarly for W2grad, b1grad, b2grad).
% 
% Stated differently, if we were using batch gradient descent to optimize the parameters,
% the gradient descent update to W1 would be W1 := W1 - alpha * W1grad, and similarly for W2, b1, b2. 
% 

Jcost = 0;%直接误差
Jweight = 0;%权值惩罚
Jsparse = 0;%稀疏性惩罚
[n m] = size(data);%m为样本的个数，n为样本的特征数

%前向算法计算各神经网络节点的线性组合值和active值
z2 = W1*data+repmat(b1,1,m);%注意这里一定要将b1向量复制扩展成m列的矩阵
a2 = sigmoid(z2);
z3 = W2*a2+repmat(b2,1,m);
a3 = sigmoid(z3);


% 计算预测产生的误差
Jcost = (0.5/m)*sum(sum((a3-data).^2));

%计算权值惩罚项
Jweight = (1/2)*(sum(sum(W1.^2))+sum(sum(W2.^2)));

%计算稀释性规则项
rho = (1/m).*sum(a2,2)  ;%求出第一个隐含层的平均值向量
Jsparse = sum(sparsityParam.*log(sparsityParam./rho)+ ...
        (1-sparsityParam).*log((1-sparsityParam)./(1-rho)));

%损失函数的总表达式
cost = Jcost+lambda*Jweight+beta*Jsparse;

%反向算法求出每个节点的误差值
d3 = -(data-a3).*(a3.*(1-a3));
sterm = beta*(-sparsityParam./rho+(1-sparsityParam)./(1-rho));%因为加入了稀疏规则项，所以
                                                             %计算偏导时需要引入该项 
d2 = (W2‘*d3+repmat(sterm,1,m)).*(a2.*(1-a2)); 

%计算W1grad 
W1grad = W1grad+d2*data‘;
W1grad = (1/m)*W1grad+lambda*W1;

%计算W2grad  
W2grad = W2grad+d3*a2‘;
W2grad = (1/m).*W2grad+lambda*W2;

%计算b1grad 
b1grad = b1grad+sum(d2,2);
b1grad = (1/m)*b1grad;%注意b的偏导是一个向量，所以这里应该把每一行的值累加起来

%计算b2grad 
b2grad = b2grad+sum(d3,2);
b2grad = (1/m)*b2grad;


%-------------------------------------------------------------------
% After computing the cost and gradient, we will convert the gradients back
% to a vector format (suitable for minFunc).  Specifically, we will unroll
% your gradient matrices into a vector.

grad = [W1grad(:) ; W2grad(:) ; b1grad(:) ; b2grad(:)];

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)        % 定义sigmoid函数
  
    sigm = 1 ./ (1 + exp(-x));
end

function numgrad = computeNumericalGradient(J, theta)
% numgrad = computeNumericalGradient(J, theta)
% theta: a vector of parameters
% J: a function that outputs a real-number. Calling y = J(theta) will return the
% function value at theta. 
  
% Initialize numgrad with zeros
numgrad = zeros(size(theta));

%% ---------- YOUR CODE HERE --------------------------------------
% Instructions: 
% Implement numerical gradient checking, and return the result in numgrad.  
% (See Section 2.3 of the lecture notes.)
% You should write code so that numgrad(i) is (the numerical approximation to) the 
% partial derivative of J with respect to the i-th input argument, evaluated at theta.  
% I.e., numgrad(i) should be the (approximately) the partial derivative of J with 
% respect to theta(i).
%                
% Hint: You will probably want to compute the elements of numgrad one at a time. 

epsilon = 1e-4;
n = size(theta,1);
E = eye(n);
for i = 1:n
    delta = E(:,i)*epsilon;
    numgrad(i) = (J(theta+delta)-J(theta-delta))/(epsilon*2.0);
end


%% ---------------------------------------------------------------
end