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- 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.
- %
- temp_y = zeros(m,num_labels);
- for i = 1 : m
- temp_y(i,y(i)) = 1;
- end
- p = zeros(size(X, 1), 1);
- X = [ones(m, 1), X];
- a2 = sigmoid(X * Theta1');
- a2 = [ones(m, 1), a2];
- hx = sigmoid(a2 * Theta2');
- %无需对hx的结果进行统一化（提取max），因为hx对每一个值的预估都是有用的数据，可以用来计算J
- J = 1 / m * sum(sum(-temp_y .* log(hx) - (1 - temp_y) .* log(1 - hx))) + lambda / (2 * m) * (sum((Theta1(:, 2:end) .^ 2)(:)) + (sum((Theta2(:, 2:end) .^ 2)(:))));
- delta_3 = hx - temp_y;
- delta_2 = delta_3 * Theta2.* a2 .* (1 - a2);
- delta_2 = delta_2(:, 2:end);
- Theta2_grad = 1 / m * (Theta2_grad + delta_3' * a2);
- Theta1_grad = 1 / m * (Theta1_grad + delta_2' * X);
- %Regularized Neural Networks
- Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + lambda / m * (Theta2(:, 2:end));
- Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + lambda / m * (Theta1(:, 2:end));
-
-
- % -------------------------------------------------------------
-
- % =========================================================================
-
- % Unroll gradients
- grad = [Theta1_grad(:) ; Theta2_grad(:)];
-
-
- end
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