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手在键盘敲很轻


机器学习(coursera 斯坦福)第五周编程作业

Preface

本文是机器学习第五周的编程作业答案记录,完整题目以及代码见github

此外还记录我在人工智能吧看到的一篇讲解神经网络的精品帖子的部分搬运。贴吧真是大佬多啊orz


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作业答案

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.
%

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

a1 = [ones(m,1) X];
z2 = a1 * Theta1';
a2 = sigmoid(z2);
a2 = [ones(m,1) a2];
a3 = sigmoid(a2 * Theta2');

% 这里不知道为什么用向量的形式写出来是不对的?
%J = 1 / m * (-ylable' * log(a3) - (1 - ylable') * log(1 - a3));
J = 1 / m * sum( sum( -ylable.* log(a3) - (1-ylable).*log(1-a3) ));

% pay attention :" Theta1(:,2:end) " , no "Theta1" .
regularized = lambda/(2*m) * (sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2)) );

J = J + regularized;



delta3 = a3-ylable; %5000x10


delta2 = delta3 * Theta2 ;
delta2 = delta2(:,2:end);

delta2 = delta2 .* sigmoidGradient(z2); %5000x25


Delta_1 = zeros(size(Theta1));
Delta_2 = zeros(size(Theta2));


Delta_1 = Delta_1 + delta2' * a1 ;

Delta_2 = Delta_2 + delta3' * a2 ;


Theta1_grad = 1/m * Delta_1;
Theta2_grad = 1/m * Delta_2;


regularized_1 = lambda/m * Theta1;
regularized_2 = lambda/m * Theta2;

% j = 0是不需要正则化的
regularized_1(:,1) = zeros(size(regularized_1,1),1);
regularized_2(:,1) = zeros(size(regularized_2,1),1);

Theta1_grad = Theta1_grad + regularized_1;
Theta2_grad = Theta2_grad + regularized_2;



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

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


end

sigmoidGradient.m

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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

randInitializeWeights.m

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function W = randInitializeWeights(L_in, L_out)
%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
%incoming connections and L_out outgoing connections
% W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights
% of a layer with L_in incoming connections and L_out outgoing
% connections.
%
% Note that W should be set to a matrix of size(L_out, 1 + L_in) as
% the first column of W handles the "bias" terms
%

% You need to return the following variables correctly
W = zeros(L_out, 1 + L_in);

% ====================== YOUR CODE HERE ======================
% Instructions: Initialize W randomly so that we break the symmetry while
% training the neural network.
%
% Note: The first column of W corresponds to the parameters for the bias unit
%


epsilon_init = 0.12;
W = rand(L_out, 1 + L_in) * 2 * epsilon_init − epsilon_init;

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

end

贴吧搬运 

参考这个帖子,仅供参考机器学习入门——浅谈神经网络

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这里介绍的是计算完一条记录,就马上更新权重,以后每计算完一条都即时更新权重。实际上批量更新的效果会更好,方法是在不更新权重的情况下,把记录集的每条记录都算过一遍,把要更新的增值全部累加起来求平均值,然后利用这个平均值来更新一次权重,然后利用更新后的权重进行下一轮的计算,这种方法叫批量梯度下降(Batch Gradient Descent)。


参考

机器学习入门——浅谈神经网络
machine-learning第五周 上机作业
Coursera吴恩达机器学习课程 总结笔记及作业代码——第5周神经网络续

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