吴恩达 机器学习 神经网络编程代码练习笔记

编程要求：

In this exercise, you will implement the backpropagation algorithm for neural networks and apply it to the task of hand-written digit recognition.

1.总体的思路

1.确定layer的层数，和每层layer的大小，这里确定包含最基本的三层结构（输入，隐含，输出）

2.随机初始化参数的大小

3.计算costfuntion，和神经网络各层的参数偏导（BP实现的过程）（梯度下降法）

4.利用梯度下降法（Matlab中用fminuc或fmincg（较fminuc快））多次迭代，求出参数

5.利用偏导的数学定义与用BP实现的偏导作比较，确保BP的过程是正确的

6.最后计算预测的准确率

2.关键代码段

1.初始化各层的参数

function W = randInitializeWeights(L_in, L_out)

W = zeros(L_out, 1 + L_in);

epsion_init = 0.12;
W = rand(L_out,L_in+1)*2*epsion_init - epsion_init;

end

2.计算代价函数和利用BP求偏导

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));

m = size(X, 1);

X = [ones(m,1) X];
HidenOutput = sigmoid(X*Theta1');%z2=a1*theta1;  a2=sigmoid(z2);
HidenOutput = [ones(m,1) HidenOutput];%train_size*hiddenlayer_size+1
Hx = sigmoid(HidenOutput*Theta2');%train_size*outputsize;

Y=zeros(m,num_labels);%train_size*10
for c =1:num_labels
    y_temp=(y==c);
    Y(:,c) = y_temp;
    J = J+sum(-y_temp'*log(Hx(:,c))-(1-y_temp)'*log(1-Hx(:,c)));
end

%regulation

J=J/m+lambda*(sum(sum(Theta1(:,2:end).^2))+sum(sum(Theta2(:,2:end).^2)))/(2*m);

%BP的实现过程
det3 =Hx - Y;%train_szie*outputSize
det2 =det3*Theta2.* sigmoidGradient([ones(m,1) X*Theta1']);%train_size*hiddenlayer_size+1
det2 = det2(:,2:end);%train_size*hiddenlayer_size
%det2 =det3*Theta2(:,2:end).* sigmoidGradient(X*Theta1');

Theta1_grad =  (det2'*X)/m;%hiddenlayer_size*inputlayer_size
Theta1_grad(:,2:end) =Theta1_grad(:,2:end)+lambda*Theta1(:,2:end)/m;

Theta2_grad =  (det3'*HidenOutput)/m;%outputsize*(hiddenlayer_size+1)
Theta2_grad(:,2:end) =Theta2_grad(:,2:end)+lambda*Theta2(:,2:end)/m;
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end

3.利用偏导的定义，检查BP

function numgrad = computeNumericalGradient(J, theta)
numgrad = zeros(size(theta));
perturb = zeros(size(theta));
e = 1e-4;
for p = 1:numel(theta)
    % Set perturbation vector
  perturb(p) = e;
  loss1 = J(theta - perturb);
  loss2 = J(theta + perturb);
   % Compute Numerical Gradient
  numgrad(p) = (loss2 - loss1) / (2*e);
  perturb(p) = 0;

end

4.训练和预测

[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);

pred = predict(Theta1, Theta2, X);

fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);