机器学习作业（三）多类别分类与神经网络——Matlab实现

题目太长了！下载地址【传送门】

第1题

简述：识别图片上的数字。

第1步：读取数据文件：

%% 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)

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

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);
sel = X(rand_indices(1:100), :);

displayData(sel);

第2步：实现displayData函数：

function [h, display_array] = displayData(X, example_width)

% Set example_width automatically if not passed in
if ~exist('example_width', 'var') || isempty(example_width) 
	example_width = round(sqrt(size(X, 2)));
end

% Gray Image
colormap(gray);

% Compute rows, cols
[m n] = size(X);
example_height = (n / example_width);

% Compute number of items to display
display_rows = floor(sqrt(m));
display_cols = ceil(m / display_rows);

% Between images padding
pad = 1;

% Setup blank display
display_array = - ones(pad + display_rows * (example_height + pad), ...
                       pad + display_cols * (example_width + pad));

% Copy each example into a patch on the display array
curr_ex = 1;
for j = 1:display_rows
	for i = 1:display_cols
		if curr_ex > m, 
			break; 
		end
		% Copy the patch
		
		% Get the max value of the patch
		max_val = max(abs(X(curr_ex, :)));
		display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ...
		              pad + (i - 1) * (example_width + pad) + (1:example_width)) = ...
						reshape(X(curr_ex, :), example_height, example_width) / max_val;
		curr_ex = curr_ex + 1;
	end
	if curr_ex > m, 
		break; 
	end
end

% Display Image
h = imagesc(display_array, [-1 1]);

% Do not show axis
axis image off

drawnow;

end

运行结果：

第3步：计算θ：

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

其中oneVsAll函数：

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

% 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];

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

第4步：实现lrCostFunction函数：

function [J, grad] = lrCostFunction(theta, X, y, lambda)

% 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));

theta2 = theta(2:end,1);
h = sigmoid(X*theta);
J = 1/m*(-y'*log(h)-(1-y')*log(1-h)) + lambda/(2*m)*sum(theta2.^2);
theta(1,1) = 0;
grad = 1/m*(X'*(h-y)) + lambda/m*theta;

grad = grad(:);

end

第5步：实现sigmoid函数：

function g = sigmoid(z)
g = 1.0 ./ (1.0 + exp(-z));
end

第6步：计算预测的准确性：

pred = predictOneVsAll(all_theta, X);
fprintf('
Training Set Accuracy: %f
', mean(double(pred == y)) * 100);

其中predictOneVsAll函数：

function p = predictOneVsAll(all_theta, X)

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];

g = zeros(size(X, 1), num_labels); 
for c = 1: num_labels,
    theta = all_theta(c, :);
    g(:, c) = sigmoid(X*theta');
end

[value, p] = max(g, [], 2);

end

　　

运行结果：

第2题

简介：使用神经网络实现数字识别（Θ已提供）

第1步：读取文档数据：

%% 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)

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

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, :));

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

　　

第2步：实现神经网络：

pred = predict(Theta1, Theta2, X);

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

其中predict函数：

function p = predict(Theta1, Theta2, X)

% 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);


X = [ones(m,1) X];
z2 = X*Theta1';
a2 = sigmoid(z2);
a2 = [ones(size(a2, 1), 1) a2];
z3 = a2*Theta2';
a3 = sigmoid(z3)
[values, p] = max(a3, [], 2)

end

运行结果：

第3步：实现单个数字识别：

rp = randperm(m);

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

    pred = predict(Theta1, Theta2, X(rp(i),:));
    fprintf('
Neural Network Prediction: %d (digit %d)
', pred, mod(pred, 10));
    
    % Pause with quit option
    s = input('Paused - press enter to continue, q to exit:','s');
    if s == 'q'
      break
    end
end

运行结果：