Coursera机器学习-Week 4-编程作业:Multi-class Classification and Neural Networks

这周入职开始工作了，周末也要重新规划了……不知道以后还有没有周末了。

这周的任务是处理分类器，一共十个数字， 0∼9 0 ∼ 9 ，需要识别手写数字。任务提供了很多训练数据，每个数据都是来自于 20∗20 20 ∗ 20 像素的图片，构成一个 1∗400 1 ∗ 400 的向量。

另外， y y 是对应的数字的状态，而 0 $0$ 会映射成 10 10 。

1.3.3 lrCostFunction.m

这个部分和上周的作业一样，是一个加上正则化处理的代价和梯度函数。不再赘述……

function [J, grad] = lrCostFunction(theta, X, y, lambda)
%LRCOSTFUNCTION Compute cost and gradient for logistic regression with 
%regularization
%   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Hint: The computation of the cost function and gradients can be
%       efficiently vectorized. For example, consider the computation
%
%           sigmoid(X * theta)
%
%       Each row of the resulting matrix will contain the value of the
%       prediction for that example. You can make use of this to vectorize
%       the cost function and gradient computations. 
%
% Hint: When computing the gradient of the regularized cost function, 
%       there're many possible vectorized solutions, but one solution
%       looks like:
%           grad = (unregularized gradient for logistic regression)
%           temp = theta; 
%           temp(1) = 0;   % because we don't add anything for j = 0  
%           grad = grad + YOUR_CODE_HERE (using the temp variable)
%

% X: m * n theta: n * 1 h_theta: m * 1
h_theta = sigmoid(X * theta);

% y: m * 1
J = (-y' * log(h_theta) - (1 - y)' * log(1 - h_theta)) / m + ...
    lambda * (theta' * theta - (theta(1, 1))^2) / (2 * m);
theta(1) = 0;
grad = (X' * (h_theta - y) + theta * lambda) / m;

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

grad = grad(:);

end

1.4 oneVsAll.m

这部分是针对每个分类进行训练，对于每个部分进行训练时，对应部分的 y y 置为 1 $1$，其他置为 0 0 。在 Example Code $ExampleCode$ 的基础上加一个循环就可以了。

function [all_theta] = oneVsAll(X, y, num_labels, lambda)
%ONEVSALL trains multiple logistic regression classifiers and returns all
%the classifiers in a matrix all_theta, where the i-th row of all_theta 
%corresponds to the classifier for label i
%   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
%   logistic regression classifiers and returns each of these classifiers
%   in a matrix all_theta, where the i-th row of all_theta corresponds 
%   to the classifier for label i

% Some useful variables
m = size(X, 1);
n = size(X, 2);

% You need to return the following variables correctly 
all_theta = zeros(num_labels, n + 1);

% Add ones to the X data matrix
X = [ones(m, 1) X];

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the following code to train num_labels
%               logistic regression classifiers with regularization
%               parameter lambda. 
%
% Hint: theta(:) will return a column vector.
%
% Hint: You can use y == c to obtain a vector of 1's and 0's that tell you
%       whether the ground truth is true/false for this class.
%
% Note: For this assignment, we recommend using fmincg to optimize the cost
%       function. It is okay to use a for-loop (for c = 1:num_labels) to
%       loop over the different classes.
%
%       fmincg works similarly to fminunc, but is more efficient when we
%       are dealing with large number of parameters.
%
% Example Code for fmincg:
%
%     % Set Initial theta
%     initial_theta = zeros(n + 1, 1);
%     
%     % Set options for fminunc
%     options = optimset('GradObj', 'on', 'MaxIter', 50);
% 
%     % Run fmincg to obtain the optimal theta
%     % This function will return theta and the cost 
%     [theta] = ...
%         fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
%                 initial_theta, options);
%

% initial theta
h_theta = zeros(n + 1, 1);

options = optimset('GradObj', 'on', 'MaxIter', 50);

for i = 1 : num_labels
    all_theta(i, :) = ... 
        fmincg(@(t)(lrCostFunction(t, X, (y == i), lambda)), h_theta, options);

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

end

1.4.1 predictOneVsAll.m

max() m a x ( ) 返回每行最大值的 index i n d e x ，而这个 index i n d e x 对应的就是我们的预测值。

function p = predictOneVsAll(all_theta, X)
%PREDICT Predict the label for a trained one-vs-all classifier. The labels 
%are in the range 1..K, where K = size(all_theta, 1). 
%  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
%  for each example in the matrix X. Note that X contains the examples in
%  rows. all_theta is a matrix where the i-th row is a trained logistic
%  regression theta vector for the i-th class. You should set p to a vector
%  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
%  for 4 examples) 

m = size(X, 1);
num_labels = size(all_theta, 1);

% You need to return the following variables correctly 
p = zeros(size(X, 1), 1);

% Add ones to the X data matrix
X = [ones(m, 1) X];

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
%               your learned logistic regression parameters (one-vs-all).
%               You should set p to a vector of predictions (from 1 to
%               num_labels).
%
% Hint: This code can be done all vectorized using the max function.
%       In particular, the max function can also return the index of the 
%       max element, for more information see 'help max'. If your examples 
%       are in rows, then, you can use max(A, [], 2) to obtain the max 
%       for each row.
%       

[K, i] = max(sigmoid(X * all_theta'), [], 2);
p = i;

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

end

2.2 predict.m

一个三层的神经网络……

function p = predict(Theta1, Theta2, X)
%PREDICT Predict the label of an input given a trained neural network
%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
%   trained weights of a neural network (Theta1, Theta2)

% Useful values
m = size(X, 1);
num_labels = size(Theta2, 1);

% You need to return the following variables correctly 
p = zeros(size(X, 1), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
%               your learned neural network. You should set p to a 
%               vector containing labels between 1 to num_labels.
%
% Hint: The max function might come in useful. In particular, the max
%       function can also return the index of the max element, for more
%       information see 'help max'. If your examples are in rows, then, you
%       can use max(A, [], 2) to obtain the max for each row.
%

X = [ones(m, 1) X];

lay2 = sigmoid(X * Theta1');
lay2 = [ones(size(lay2, 1), 1) lay2];
lay3 = sigmoid(lay2 * Theta2');
[a, b] = max(lay3, [], 2);

p = b;

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

end

结果

代码亲测，都是可以通过测试的。

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