神经网络作业: NN LEARNING Coursera Machine Learning（Andrew Ng） WEEK 5

在WEEK 5中，作业要求完成通过神经网络(NN)实现多分类的逻辑回归(MULTI-CLASS LOGISTIC REGRESSION)的监督学习(SUOERVISED LEARNING)来识别阿拉伯数字。作业主要目的是感受如何在NN中求代价函数（COST FUNCTION）和其假设函数中各个参量(THETA)的求导值（GRADIENT DERIVATIVE)（利用BACKPROPAGGATION）。

难度不高，但问题是你要习惯使用MATLAB的矩阵QAQ，作为一名蒟蒻，我已经狗带了。以下代核心部分的代码希望给被作业卡住的同学一些帮助。但请不要照搬代码哦~不要~不要~

ty = zeros(m, num_labels);

for i=1:m
    for j=1:num_labels
        if y(i)==j
            ty(i,j) = 1;
        end
    end
end

a1 = X;
a1 = [ones(size(a1,1),1) a1];
z2 = a1 * Theta1';
a2 = sigmoid(z2);
a2 = [ones(size(a2,1),1) a2];
z3 = a2 * Theta2';
a3 = sigmoid(z3);


for i=1:m
    for j=1:num_labels
        J = J - log(1-a3(i,j))*(1-ty(i,j))/m-log(a3(i,j))*ty(i,j)/m;
    end
end

%size(J,1)
%size(J,2)
    
d3 = a3 - ty;
d2 = (d3 * Theta2(:,2:end)).*sigmoidGradient(z2);
Theta1_grad = Theta1_grad + d2'*a1/m;
Theta2_grad = Theta2_grad + d3'*a2/m;

% -------------------------------------------------------------
JJ=0;

 for i=1:size(Theta1,1)
    for j=2:size(Theta1,2)
                JJ = JJ + Theta1(i,j)*Theta1(i,j)*lambda/(m*2);
    end
 end
 size(Theta1,1);
 size(Theta1,2);
 
 for i=1:size(Theta2,1)
       for j=2:size(Theta2,2)
           JJ = JJ + Theta2(i,j)*Theta2(i,j)*lambda/(2*m);
      end
end
size(Theta2,1);
size(Theta2,2);
%J = J + (lambda/(2*m)) * (Theta1(:,2:end).*Theta1(:,2:end)+Theta2(2:end,:).*Theta2(2:end,:));
J =J+JJ;

Theta1_gradd = zeros(size(Theta1));
Theta2_gradd = zeros(size(Theta2));

for i=2:size(Theta1,2)
    for j=1:size(Theta1,1)
        Theta1_gradd(j,i) = Theta1(j,i)*lambda/m;
    end
end

for i=2:size(Theta2,2)
    for j=1:size(Theta2,1)
        Theta2_gradd(j,i) = Theta2(j,i)*lambda/m;
    end
end

Theta1_grad = Theta1_gradd+Theta1_grad;
Theta2_grad = Theta2_gradd+Theta2_grad;

PS:博主蒟蒻强迫自己下次要写矩阵运算，不能再套循环啦！！！