vectorize

[webbp]

If you vectorize cost and backprop, 50 epochs takes 2.4 seconds instead of 150 seconds.

Vectorized cost: replace this loop with

yy = zeros(size(y,1),num_labels);
yy(sub2ind(size(yy),1:length(y),y'))=1;
J = sum(sum(- yy .* log(a3) - (1 - yy) .* log(1 - a3)))/m;

Vectorized backprop: replace this loop with

d3 = a3 - yy;
d2 = (d3 * Theta2) .* [ones(m, 1) sigmoidGradient(z2)];
d2 = d2(:,2:end);
Theta1_grad = d2' * a1;
Theta2_grad = d3' * a2;

[Zhenye-Na]

Do you wanna make a PR?