Andrew Ng coursera上的《机器学习》ex4
2016-08-23 11:18
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Andrew Ng coursera上的《机器学习》ex4
按照课程所给的ex4的文档要求,ex4要求完成以下几个计算过程的代码编写:exerciseName | description |
---|---|
sigmoidGradient.m | compute the grident of the sigmoid function |
randInitializedWeights.m | randomly initialize weights |
nnCostFunction.m | Neutral network function |
1.sigmoidGradient.m
要求如下:根据作业文档给出的要求以及逻辑回归的梯度下降的表达式。得出如下的Octave代码:
function g = sigmoidGradient(z) %SIGMOIDGRADIENT returns the gradient of the sigmoid function %evaluated at z % g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function % evaluated at z. This should work regardless if z is a matrix or a % vector. In particular, if z is a vector or matrix, you should return % the gradient for each element. g = zeros(size(z)); % ====================== YOUR CODE HERE ====================== % Instructions: Compute the gradient of the sigmoid function evaluated at % each value of z (z can be a matrix, vector or scalar). g = sigmoid(z) .* (1 - sigmoid(z)); % ============================================================= end
需要注意的是文档中给出的表达式只是针对一个训练数据集的,需要对所有的训练数据集进行操作的话,需要用到Octave的一个运算符.,小数点表示对所有数据都进行操作。
2. randInitializedWeights.m
该块代码不需要自己写,所有忽略。3.nnCostFunction.m
要求如下:Octave代码如下:
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. % a1 = [ones(m, 1) X]; z2 = a1 * Theta1'; a2 = sigmoid(z2); a2 = [ones(m, 1) a2]; z3 = a2 * Theta2'; h = sigmoid(z3); yk = zeros(m, num_labels); for i = 1:m yk(i, y(i)) = 1; end J = (1/m)* sum(sum(((-yk) .* log(h) - (1 - yk) .* log(1 - h)))); r = (lambda / (2 * m)) * (sum(sum(Theta1(:, 2:end) .^ 2)) + sum(sum(Theta2(:, 2:end) .^ 2))); J = J + r; for row = 1:m a1 = [1 X(row,:)]'; z2 = Theta1 * a1; a2 = sigmoid(z2); a2 = [1; a2]; z3 = Theta2 * a2; a3 = sigmoid(z3); z2 = [1; z2]; delta3 = a3 - yk'(:, row); delta2 = (Theta2' * delta3) .* sigmoidGradient(z2); delta2 = delta2(2:end); Theta1_grad = Theta1_grad + delta2 * a1'; Theta2_grad = Theta2_grad + delta3 * a2'; end Theta1_grad = Theta1_grad ./ m; Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) ... + (lambda/m) * Theta1(:, 2:end); Theta2_grad = Theta2_grad ./ m; Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + ... + (lambda/m) * Theta2(:, 2:end); % ------------------------------------------------------------- % ========================================================================= % Unroll gradients grad = [Theta1_grad(:) ; Theta2_grad(:)]; end
以上的代码分成了三个部分:
Part 1: Feedforward the neural network and return the cost in the variable J。
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.
关于反向传播的思想如下:
Part 3: Implement regularization with the cost function and gradients.
三个部分分别对应着不同的代码,上面的代码从上往下依次为Part1,part2,part3。
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