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ds/25-1/r/12.1/mlclass-ex4/nnCostFunction.m

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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.
+%
+
+%feedforward propagation
+X = [ones(m, 1) X];
+
+z2 = X * Theta1';
+a2 = sigmoid(z2);
+a2 = [ones(m, 1) a2];
+
+z3 = a2 * Theta2';
+a3 = sigmoid(z3);
+
+% one hot encoding
+y_matrix = eye(num_labels)(y, :);
+
+%sum m - обучающие параметры
+%sum K - по классам (выходным нейронам)
+J = (1/m) * sum(sum(-y_matrix .* log(a3) - (1 - y_matrix) .* log(1 - a3)));
+
+reg_term = (lambda/(2*m)) * (sum(sum(Theta1(:, 2:end).^2)) + sum(sum(Theta2(:, 2:end).^2)));
+J = J + reg_term;
+
+Delta1 = zeros(size(Theta1));
+Delta2 = zeros(size(Theta2));
+
+for t = 1:m
+    %feedforward propagation
+    a1 = X(t, :)';
+    z2 = Theta1 * a1;
+    a2 = [1; sigmoid(z2)];
+
+    z3 = Theta2 * a2;
+    a3 = sigmoid(z3);
+
+    %difference between the network’s activation and the true target value
+    delta3 = a3 - y_matrix(t, :)';
+
+    delta2 = (Theta2' * delta3) .* [1; sigmoidGradient(z2)];
+    delta2 = delta2(2:end);
+
+    %measures how much that node was “responsible” for any errors in our output.
+    Delta1 = Delta1 + delta2 * a1';
+    Delta2 = Delta2 + delta3 * a2';
+end
+
+%divide the accumulated gradients by m to obtain the gradients for the neural network cost function.
+Theta1_grad = Delta1 / m;
+Theta2_grad = Delta2 / m;
+
+Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + (lambda/m) * Theta1(:, 2:end);
+Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + (lambda/m) * Theta2(:, 2:end);
+
+
+
+
+
+
+
+
+
+
+
+
+
+% -------------------------------------------------------------
+
+% =========================================================================
+
+% Unroll gradients
+grad = [Theta1_grad(:) ; Theta2_grad(:)];
+
+
+end