机器学习：使用matlab实现逻辑回归解决数字识别（多元分类）问题_matlab 逻辑回归

前置章节

二元分类问题的逻辑回归包含原理及实现。

这次做多元分类，目的是能够识别$20\times 20$像素的手写体数字。

数据载入

来自MINST的手写数字数据库，矩阵X中是5000张图片的灰度构成的数据集，因为图片像素是20×20，所以矩阵每行有400个元素，为图片的灰度。y向量表明图片中的数字是什么，因为matlab数组下标从1开始，所以我们把数字0对应的数据映射到10上。

% Load saved matrices from file
load('ex3data1.mat');
% The matrices X and y will now be in your MATLAB environment
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数据可视化

随机抽出几张图片瞅一瞅，吴恩达的代码没仔细研究，先放在这里：

function [h, display_array] = displayData(X, example_width)
%DISPLAYDATA Display 2D data in a nice grid
%   [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data
%   stored in X in a nice grid. It returns the figure handle h and the 
%   displayed array if requested.

% 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
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m = size(X, 1);
% Randomly select 100 data points to display
rand_indices = randperm(m);
sel = X(rand_indices(1:100), :);
displayData(sel);
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代价-梯度函数

ex3的意思是在ex2的基础上让代价-梯度函数向量化，即通过矩阵运算省略for循环，不过我已经在ex2搞定了