吴恩达老师机器学习ex3.Multi-class Classification and Neural Networks

吴恩达 机器学习 第四周作业 Multi-class Classification and Neural Networks

Octave代码

lrCostFunction.m

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)
%
h = 1 ./ (1 + exp(-X * theta));
theta_temp = theta(2 : length(theta), 1);
J = 1 / m * sum(-y .* log(h) - (1 - y) .* log(1 - h)) + 0.5 * lambda / m * sum(theta_temp .^ 2);
grad = 1 / m .* (X' * (h - y)) + lambda / m .* theta;
grad(1) = 1 / m * sum(h - y);% =============================================================grad = grad(:);end

oneVsAll.m

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);
%for c = 1 : num_labels;initial_theta = zeros(n + 1, 1);
options = optimset('GradObj', 'on', 'MaxIter', 50);
[theta, cost] =  fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
% fprintf('\ntheta: %f\n', theta);
% fprintf('\nall_theta: %f\n', all_theta);
all_theta(c, :) = theta;end;% =========================================================================end

predictOneVsAll.m

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.
%       p_temp = 1 ./ (1 + exp(-X * all_theta'));
[max_value, p] = max(p_temp, [], 2);% =========================================================================end

ex3运行结果

Octave command prompt

octave:33> ex3Loading and Visualizing Data ...
Program paused. Press enter to continue.Testing lrCostFunction() with regularization
Cost: 2.534819
Expected cost: 2.534819
Gradients:0.146561 -0.548558 0.724722 1.398003 
Expected gradients:0.146561-0.5485580.7247221.398003
Program paused. Press enter to continue.Training One-vs-All Logistic Regression...
Iteration    50 | Cost: 1.386626e-02
Iteration    50 | Cost: 5.725220e-02
Iteration    50 | Cost: 6.396625e-02
Iteration    50 | Cost: 3.633786e-02
Iteration    50 | Cost: 6.182203e-02
Iteration    50 | Cost: 2.173015e-02
Iteration    50 | Cost: 3.295401e-02
Iteration    50 | Cost: 8.460907e-02
Iteration    50 | Cost: 8.094079e-02
Iteration    50 | Cost: 9.847356e-03
Program paused. Press enter to continue.Training Set Accuracy: 95.100000
octave:34> 

predict.m

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];z2 = Theta1 * X';
a2 = 1 ./ (1 + exp(-z2));
units = size(a2, 1);
a2_new = [ones(1, m); a2];z3 = Theta2 * a2_new;
a3 = 1 ./ (1 + exp(-z3));[max_value, p] = max(a3', [], 2);% =========================================================================end

ex3_nn运行结果

Octave command prompt

octave:34> ex3_nnLoading and Visualizing Data ...
Program paused. Press enter to continue.Loading Saved Neural Network Parameters ...Training Set Accuracy: 97.520000
Program paused. Press enter to continue.Displaying Example ImageNeural Network Prediction: 5 (digit 5)
Paused - press enter to continue, q to exit: