www.gusucode.com > SAE RBM 程序MATLAB源码代码实现的一个关于sae的例子 > sparseAutoencoderLinearCost.m

    function [cost,grad] = sparseAutoencoderLinearCost(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);

%% ---------- 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. 
% 
[ndims, m] = size(data);


z2 = zeros(hiddenSize, m);
z3 = zeros(visibleSize, m);
a2 = zeros(size(z2));
% a3 = zeros(size(z3));

z2 = bsxfun(@plus, W1*data, b1);
a2 = sigmoid(z2);
z3 = bsxfun(@plus, W2*a2, b2);
% a3 = z3;


rho = zeros(hiddenSize, 1);
rho = (1. / m) * sum(a2, 2);
sp = sparsityParam;
sparsity_delta = -sp ./ rho + (1-sp) ./ (1-rho);

delta3 = -(data - z3);
% delta2 = ( W2' * delta3 + beta * repmat(sparsity_delta, 1, m)) .* sigmoidGrad(z2);
delta2 = bsxfun(@plus, W2' * delta3, beta * sparsity_delta) .* sigmoidGrad(z2);

clear z2;
% clear z3;
% 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));


W1grad = (1. / m) * (delta2 * data') + lambda * W1;
b1grad = (1. / m) * sum(delta2, 2);
W2grad = (1. / m) * delta3 * a2' + lambda * W2;
b2grad = (1. / m) * sum(delta3, 2);

clear delta2;
clear delta3;
clear a2;

cost = (1. / m) * sum((1. / 2) * sum((z3 - data).^2)) + ...
    (lambda / 2.) * (sum(sum(W1.^2)) + sum(sum(W2.^2))) + ...
    beta * sum( sp*log(sp./rho) + (1-sp)*log((1-sp)./(1-rho)) );

memory

function grad = sigmoidGrad(x)
    e_x = exp(-x);
    grad = e_x ./ ((1 + e_x).^2); 
end



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