吴恩达机器学习练习3——多元分类与神经网络

Logistic回归——手写数字识别

可视化数据集

该训练样本为5,000张20*20的书写数字的灰度图。

X：5000*400
y : 5000*1
在X中随机选取100张图像并显示

function [h, display_array] = displayData(X, example_width)
if ~exist('example_width', 'var') || isempty(example_width) 
	example_width = round(sqrt(size(X, 2)));
end
colormap(gray);
[m n] = size(X);
example_height = (n / example_width);
display_rows = floor(sqrt(m));
display_cols = ceil(m / display_rows);
pad = 1;
display_array = - ones(pad + display_rows * (example_height + pad), ...
                       pad + display_cols * (example_width + pad));
curr_ex = 1;
for j = 1:display_rows
	for i = 1:display_cols
		if curr_ex > m, 
			break; 
		end
		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
h = imagesc(display_array, [-1 1]);
axis image off
drawnow;
end

代价函数和梯度下降

function [J, grad] = lrCostFunction(theta, X, y, lambda)
	m = length(y); 
	J = 0;
	grad = zeros(size(theta));
	J = (1/m)*(-y'*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta)))+lambda/2/m*sum(theta(2:end).^2);
	temp = theta; 
	temp(1) = 0;
	grad = (1/m)*(X'*(sigmoid(X*theta)-y))+lambda/m*temp;
	grad = grad(:);%21*1

end

一对多

function [all_theta] = oneVsAll(X, y, num_labels, lambda)
		m = size(X, 1);%5000
		n = size(X, 2);%20
		all_theta = zeros(num_labels, n + 1);%10*21
		X = [ones(m, 1) X];    %5000*21
		options = optimset('GradObj', 'on', 'MaxIter', 50);
	for i = 1: num_labels
		 all_theta(i,:) = fmincg (@(t)(lrCostFunction(t, X, (y == i), lambda)), all_theta(i,:)', options);
end

预测

function p = predictOneVsAll(all_theta, X)
	m = size(X, 1);
	num_labels = size(all_theta, 1);
	p = zeros(size(X, 1), 1);
	X = [ones(m, 1) X];
	[r, p] = max(X * all_theta', [], 2);
end