Neural Network Cost Function

nnCostFunction.m

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 network
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));

% ====================== 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.
%


X = [ones(m, 1) X];
y = eye(num_labels)(y,:);


a1 = X;

z2 = a1 * Theta1';
a2 = sigmoid(z2);

n = size(a2, 1);
a2 = [ones(n,1) a2];

z3 = a2 * Theta2';
a3 = sigmoid(z3);

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

J = ((1/m) * sum(sum((-y .* log(a3))-((1-y) .* log(1-a3))))) + regularization;


delta_3 = a3 - y;
delta_2 = (delta_3 * Theta2(:,2:end)) .* sigmoidGradient(z2);


delta_cap2 = delta_3' * a2; 
delta_cap1 = delta_2' * a1;

Theta1_grad = ((1/m) * delta_cap1) + ((lambda/m) * (Theta1));
Theta2_grad = ((1/m) * delta_cap2) + ((lambda/m) * (Theta2));

Theta1_grad(:,1) -= ((lambda/m) * (Theta1(:,1)));
Theta2_grad(:,1) -= ((lambda/m) * (Theta2(:,1)));



% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end

if you have some idea regarding conjugate gradient descent to optimize the value of Theta1 and Theta2 please share me your concept.

Not anything specific at the moment.

On Monday, July 30, 2012, Shishir01 wrote: if you have some idea regarding conjugate gradient descent to optimize the value of Theta1 and Theta2 please share me your concept. --- Reply to this email directly or view it on GitHub: https://gist.github.com/1360709

##

…

--Regards, Denzil

with this function how to draw performance plot?

y = eye(num_labels)(y,:);
this line giving me error in matlab. How to correct this

ey = eye(num_labels);
y = ey(y,:);

if y = [1;1;0;0;0;0;0;0;1;1]

ey = eye(num_labels);
y = ey(y,:);

will wrong