Machine Learning week 4 quiz: programming assignment-Multi-class Classification and Neural Networks

一、ex3.m

%% Machine Learning Online Class - Exercise 3 | Part 1: One-vs-all

% Instructions
% ------------
%
% This file contains code that helps you get started on the
% linear exercise. You will need to complete the following functions
% in this exericse:
%
% lrCostFunction.m (logistic regression cost function)
% oneVsAll.m
% predictOneVsAll.m
% predict.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%

%% Initialization
clear ; close all; clc

%% Setup the parameters you will use for this part of the exercise
input_layer_size = 400; % 20x20 Input Images of Digits
num_labels = 10; % 10 labels, from 1 to 10
% (note that we have mapped "0" to label 10)

%% =========== Part 1: Loading and Visualizing Data =============
% We start the exercise by first loading and visualizing the dataset.
% You will be working with a dataset that contains handwritten digits.
%

% Load Training Data
fprintf('Loading and Visualizing Data ...\n')

load('ex3data1.mat'); % training data stored in arrays X, y
m = size(X, 1);

% Randomly select 100 data points to display
rand_indices = randperm(m); % Randomly select 100
sel = X(rand_indices(1:100), :);

displayData(sel);

fprintf('Program paused. Press enter to continue.\n');
pause;

%% ============ Part 2: Vectorize Logistic Regression ============
% In this part of the exercise, you will reuse your logistic regression
% code from the last exercise. You task here is to make sure that your
% regularized logistic regression implementation is vectorized. After
% that, you will implement one-vs-all classification for the handwritten
% digit dataset.
%

fprintf('\nTraining One-vs-All Logistic Regression...\n')

lambda = 0.1;
[all_theta] = oneVsAll(X, y, num_labels, lambda);

fprintf('Program paused. Press enter to continue.\n');
pause;

%% ================ Part 3: Predict for One-Vs-All ================
% After ...
pred = predictOneVsAll(all_theta, X);

fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);

二、ex3_nn.m

%% Machine Learning Online Class - Exercise 3 | Part 2: Neural Networks

% Instructions
% ------------
%
% This file contains code that helps you get started on the
% linear exercise. You will need to complete the following functions
% in this exericse:
%
% lrCostFunction.m (logistic regression cost function)
% oneVsAll.m
% predictOneVsAll.m
% predict.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%

%% Initialization
clear ; close all; clc

%% Setup the parameters you will use for this exercise
input_layer_size = 400; % 20x20 Input Images of Digits
hidden_layer_size = 25; % 25 hidden units
num_labels = 10; % 10 labels, from 1 to 10
% (note that we have mapped "0" to label 10)

%% =========== Part 1: Loading and Visualizing Data =============
% We start the exercise by first loading and visualizing the dataset.
% You will be working with a dataset that contains handwritten digits.
%

% Load Training Data
fprintf('Loading and Visualizing Data ...\n')

load('ex3data1.mat');
m = size(X, 1);

% Randomly select 100 data points to display
sel = randperm(size(X, 1));
sel = sel(1:100);

displayData(X(sel, :));

fprintf('Program paused. Press enter to continue.\n');
pause;

%% ================ Part 2: Loading Pameters ================
% In this part of the exercise, we load some pre-initialized
% neural network parameters.

fprintf('\nLoading Saved Neural Network Parameters ...\n')

% Load the weights into variables Theta1 and Theta2
load('ex3weights.mat');

%% ================= Part 3: Implement Predict =================
% After training the neural network, we would like to use it to predict
% the labels. You will now implement the "predict" function to use the
% neural network to predict the labels of the training set. This lets
% you compute the training set accuracy.

pred = predict(Theta1, Theta2, X);

fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);

fprintf('Program paused. Press enter to continue.\n');
pause;

% To give you an idea of the network's output, you can also run
% through the examples one at the a time to see what it is predicting.

% Randomly permute examples
rp = randperm(m);

for i = 1:m
% Display
fprintf('\nDisplaying Example Image\n');
displayData(X(rp(i), :));

pred = predict(Theta1, Theta2, X(rp(i),:));
fprintf('\nNeural Network Prediction: %d (digit %d)\n', pred, mod(pred, 10));

% Pause
fprintf('Program paused. Press enter to continue.\n');
pause;
end

三、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 % m

% You need to return the following variables correctly
J = 0; %1*1
grad = zeros(size(theta)); %(n+1)*1

% ====================== 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 = sigmoid(X*theta); %m*1
part1 = y.*(log(h)); %m*1
part2 = (1-y).*(log(1-h)); %m*1

J_ori = sum(-part1 - part2) / m; %1*1

sz_theta = size(theta, 1);
theta_temp = theta(2:sz_theta);
punish_J = sum(theta_temp.^2)*lambda/2/m;
J = J_ori + punish_J;

% grad

diff = h - y; %m*1
temp = X' * diff; % (n+1)*m × m*1 -> (n+1)*1
temp = temp / m; % (n+1)*1；

grad_ori = temp;

punish_theta = theta_temp*lambda/m;
punish_theta = [0; punish_theta];
grad = grad_ori + punish_theta;

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

grad = grad(:);

end

四、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
% logisitc 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); % m
n = size(X, 2); % n

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

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

% ====================== 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 use
% 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] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
all_theta(c, :) = theta;
end

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

end

五、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); % m
num_labels = size(all_theta, 1); % k

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

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

% ====================== 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.
%

x_theta = X * all_theta'; % m*(n+1) × (n+1)*k -> m*k
for c = 1:m

max_value = max(x_theta(c,:));
idx = find(x_theta(c,:) == max_value)
p(c) = idx;

end

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

end

六、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); % m
num_labels = size(Theta2, 1); %num_labels

% You need to return the following variables correctly
p = zeros(size(X, 1), 1); % m*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]; % add 1, m*(n+1)

x_theta1 = X * Theta1'; % m*(n+1) × (n+1)*k -> m*k
x_theta1 = sigmoid(x_theta1);

x_theta1 = [ones(m, 1) x_theta1] % add 1

x_theta2 = x_theta1 * Theta2'; % m*k × k*(n+1) -> m*(n+1)
x_theta2 = sigmoid(x_theta2);

for c = 1:m

max_value = max(x_theta2(c,:));
idx = find(x_theta2(c,:) == max_value)
p(c) = idx;

end

%max_value = max(x_theta2);
%idx = find(x_theta2 == max_value);
%p = idx;

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

end

七、submit results