Machine Learning by Andrew Ng --- neural network learning

The step of this exercise is show in the pdf which i have updoaded.

Neural network of this exercise is not easy to finish,okay,let me show U.

nnCostFunction:

function [J grad] = nnCostFunction(nn_params, ...                                   input_layer_size, ...                                   hidden_layer_size, ...                                   num_labels, ...                                   X, y, lambda)%NNCOSTFUNCTION Implements the neural network cost function for a two layer%neural network which performs classification%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...%   X, y, lambda) computes the cost and gradient of the neural network. The%   parameters for the neural network are "unrolled" into the vector%   nn_params and need to be converted back into the weight matrices. % %   The returned parameter grad should be a "unrolled" vector of the%   partial derivatives of the neural network.%% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices% for our 2 layer neural networkTheta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...                 hidden_layer_size, (input_layer_size + 1));Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...                 num_labels, (hidden_layer_size + 1));% Setup some useful variablesm = size(X, 1);         % You need to return the following variables correctly J = 0;Theta1_grad = zeros(size(Theta1));Theta2_grad = zeros(size(Theta2));% ====================== YOUR CODE HERE ======================% Instructions: You should complete the code by working through the%               following parts.%% Part 1: Feedforward the neural network and return the cost in the%         variable J. After implementing Part 1, you can verify that your%         cost function computation is correct by verifying the cost%         computed in ex4.m%% Part 2: Implement the backpropagation algorithm to compute the gradients%         Theta1_grad and Theta2_grad. You should return the partial derivatives of%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and%         Theta2_grad, respectively. After implementing Part 2, you can check%         that your implementation is correct by running checkNNGradients%%         Note: The vector y passed into the function is a vector of labels%               containing values from 1..K. You need to map this vector into a %               binary vector of 1's and 0's to be used with the neural network%               cost function.%%         Hint: We recommend implementing backpropagation using a for-loop%               over the training examples if you are implementing it for the %               first time.%% Part 3: Implement regularization with the cost function and gradients.%%         Hint: You can implement this around the code for%               backpropagation. That is, you can compute the gradients for%               the regularization separately and then add them to Theta1_grad%               and Theta2_grad from Part 2.%%=================================Costfunction========================================X=[ones(size(X,1),1) X];a1=X;z2=Theta1*a1';a2=sigmoid(z2);a2=[ones(1,m) ; a2];z3=Theta2*a2;a3=sigmoid(z3);y_vec=zeros(num_labels,m);for index=1:my_vec(y(index),index)=1;endsize(y_vec);for index_num=1:mJ+= sum(-1*y_vec(:,index_num).*log(a3(:,index_num))-(1-y_vec(:,index_num)).*log(1-a3(:,index_num)));end J=J/m;size(J);J=J+(lambda/( 2*m )) * (sum  (sum  ( Theta1(:,2:end).^2 ) )+ sum(sum(Theta2(:,2:end).^2)) )  %===================================backprogation=======================================%Delta2=(zeros(size(Theta2))) (:,2:end);%Delta1=(zeros(size(Theta1))) (:,2:end);%for ind=1:m%delta3=a3(:,ind)-y_vec(:,ind);%delta2=sum( (Theta2'*delta3)(2:end).*sigmoidGradient(z2(:,ind)),2 );%Delta2=Delta2 + delta3*a2(2:end,ind)';%test=delta2*a1(ind,2:end);%Delta1=Delta1 + delta2*a1(ind,2:end);%endDelta1 = zeros( hidden_layer_size, (input_layer_size + 1));Delta2 = zeros( num_labels, (hidden_layer_size + 1));%Delta需要bias unit，delta不需要bias unitfor i=1:m    delta3 = a3(:,i) - y_vec(:,i);            #注意这里的δ是不包含bias unit的delta的，毕竟bias unit永远是1，      #不需要计算delta, 下面的2:end,: 过滤掉了bias unit相关值      delta2 = (Theta2'*delta3)(2:end,:).*sigmoidGradient(z2(:,i));      #移除bias unit上的delta2，但是由于上面sigmoidGradient式子中      #的z，本身不包含bias unit，所以下面的过滤不必要，注释掉。      #delta2 = delta2(2:end);      Delta2 += delta3 * a2(:,i)';            #第一层的input是一行一行的，和后面的结构不一样，后面是一列作为一个example      Delta1 += delta2 * a1(i,:); endTheta1_grad=Delta1/m;Theta2_grad=Delta2/m;Theta2_grad(:,2:end) = Theta2_grad(:,2:end) .+ lambda * Theta2(:,2:end) / m;  Theta1_grad(:,2:end) = Theta1_grad(:,2:end) .+ lambda * Theta1(:,2:end) / m; % =========================================================================% Unroll gradientsgrad = [Theta1_grad(:) ; Theta2_grad(:)];%训练集一个一个轮流训练，一次只训练一个set，前进后反向。end

sigmoidGradient:

function g = sigmoidGradient(z)%SIGMOIDGRADIENT returns the gradient of the sigmoid function%evaluated at z%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function%   evaluated at z. This should work regardless if z is a matrix or a%   vector. In particular, if z is a vector or matrix, you should return%   the gradient for each element.g = zeros(size(z));% ====================== YOUR CODE HERE ======================% Instructions: Compute the gradient of the sigmoid function evaluated at%               each value of z (z can be a matrix, vector or scalar).%g=( 1.0 ./ (1.0 .+ exp(-z)) ) *( (1.0 .- (1.0 ./ (1.0 .+ exp(-z)) ) )' );g=sigmoid(z).*(1-sigmoid(z)); 

randomInitializeWeights：

function W = randInitializeWeights(L_in, L_out)%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in%incoming connections and L_out outgoing connections%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights %   of a layer with L_in incoming connections and L_out outgoing %   connections. %%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as%   the column row of W handles the "bias" terms%% You need to return the following variables correctly W = zeros(L_out, 1 + L_in);% ====================== YOUR CODE HERE ======================% Instructions: Initialize W randomly so that we break the symmetry while%               training the neural network.%% Note: The first row of W corresponds to the parameters for the bias units%epsilon_init=0.12;W=rand(L_out,L_in+1) * 2 * epsilon_init - epsilon_init;% =========================================================================end

Tips:

1. some build-in functions in MATLAB must pass a vector of theta,rather than matrix.

2. for y,if U use BP to solve multip-classification problems,then U must change every y to vector.

3. in BP,every single traning set is pass to BP one by one .for the first one,FP using x then BP using y,the second ,third...