手写数字识别实现

function [J grad] = nnCostFunction(nn_params, … input_layer_size, … hidden_layer_size, … num_labels, … X, y, lambda) Theta1 = 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 variables m = size(X, 1); % You need to return the following variables correctly J = 0; Theta1_grad = zeros(size(Theta1)); Theta2_grad = zeros(size(Theta2)); %% 对y进行处理 Y(find(y==3))= [0 0 1 0 0 0 0 0 0 0]; 用于 Feedforward cost function 1和2 Y=[]; E = eye(num_labels); % 要满足K可以是任意，则不能写eye(10)！！ for i=1:num_labels Y0 = find(y==i); % 找到等于y=i的序列号,替换向量 Y(Y0,:) = repmat(E(i,:),size(Y0,1),1); end %% regularized Feedforward cost function lambda=1 % 计算前向传输 Add ones to the X data matrix -jin X = [ones(m, 1) X]; a2 = sigmoid(X * Theta1′); % 第二层激活函数输出 a2 = [ones(m, 1) a2]; % 第二层加入b a3 = sigmoid(a2 * Theta2′); temp1 = [zeros(size(Theta1,1),1) Theta1(:,2:end)]; % 先把theta(1)拿掉，不参与正则化 temp2 = [zeros(size(Theta2,1),1) Theta2(:,2:end)]; temp1 = sum(temp1 .^2); % 计算每个参数的平方，再就求和 temp2 = sum(temp2 .^2); cost = Y .* log(a3) + (1 – Y ) .* log( (1 – a3)); % cost是m*K(5000*10)的结果矩阵 sum(cost(:))全部求和 J= -1 / m * sum(cost(:)) + lambda/(2*m) * ( sum(temp1(:))+ sum(temp2(:)) ); %% 计算 Gradient delta_1 = zeros(size(Theta1)); delta_2 = zeros(size(Theta2)); for t = 1:m % step 1 a_1 = X(t,:)’; % a_1 = [1 ; a_1]; z_2 = Theta1 * a_1; a_2 = sigmoid(z_2); a_2 = [1 ; a_2]; z_3 = Theta2 * a_2; a_3 = sigmoid(z_3); % step 2 err_3 = zeros(num_labels,1); for k = 1:num_labels err_3(k) = a_3(k) – (y(t) == k); end % step 3 err_2 = Theta2′ * err_3; % err_2有26行！！！ err_2 = err_2(2:end) .* sigmoidGradient(z_2); % 去掉第一个误差值，减少为25. sigmoidGradient(z_2)只有25行！！！ % step 4 delta_2 = delta_2 + err_3 * a_2′; delta_1 = delta_1 + err_2 * a_1′; end % step 5 Theta1_temp = [zeros(size(Theta1,1),1) Theta1(:,2:end)]; Theta2_temp = [zeros(size(Theta2,1),1) Theta2(:,2:end)]; Theta1_grad = 1 / m * delta_1 + lambda/m * Theta1_temp; Theta2_grad = 1 / m * delta_2 + lambda/m * Theta2_temp ; % Unroll gradients grad = [Theta1_grad(:) ; Theta2_grad(:)]; end