机器学习实现线性梯度算实现octave

最近一直在查找机器学习实现之类的问题,今天正好有机会和大家共享一下.

感悟

机器学习，感到就是数值分析等数学课程在盘算机上的一个应用。让我想起了理查德.费曼说的“数学之于物理就像做爱之于手淫"那句经典的台词，呵呵。

Octave, scilab，matlab这三种数学具工，编程风格兼容，而前两者是开源，后一是要收费的,对于机器学习说来Octave已够用，所以还是选择Octave来实现吧。

这里不对机器学习的识知做过多释解，因为有个哥们讲的真是太好了：Andrew Ng。课程义讲等(Handouts and Materials)。

批量线性规划代码

##batch_gradient.m

## -*- texinfo -*-
## @deftypefn {Function File} {} [ theta ] = batch_gradient ( x, y)
## Return the parameter of linear founction where y = theta[2:n+1]*x + theta(1).
##	where n is the row of matrix x.
## It use batch gradient algorithm obviously.
## For example:
##
## @example
## @group
## x=[1 4;2 5;5 1; 4 2] y = [ 19 26 19 20]
## batch_gradient (x, y)
##   @result{} [0.0060406   2.9990063   3.9990063]
## @end group
## @end example
## @seealso{stichastic_gradient}
## @end deftypefn
## Author: xiuleili <xiuleili@XIULEILI>
## Created: 2013-04-26

function [ theta ] = batch_gradient ( x, y)
[n,m]=size(x);
[my,ny]=size(y);
theta = rand(1, m+1);
if(ny ~= n | my!= 1)
error("Error: x should be a matrix with(n,m) and y must be (1,n), where n is the count of training samples.");
end;

one = ones(n,1);
X = [one x]';
learning_rate = 0.01;
error = 1;
threshold = 0.000001;
times = 0;
start_time = clock ();
while error  > threshold
theta += learning_rate * (y - theta*X) *X';
error = sum((theta * X - y).^2) / 2;
times += 1;
printf("[%d] the current err is: %f", times, error);
disp(theta);
if(times > 10000000000)
break;
end;
end;
end_time = clock ();
disp( seconds(end_time - start_time));
endfunction

用法如图所示



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随机线性梯度源码

##stochastic_gradient.m

### -*- texinfo -*-
## @deftypefn {Function File} {} [ theta ] = stochastic_gradient ( x, y)
## Return the parameter of linear founction where y = theta[2:n+1]*x + theta(1).
##	where n is the row of matrix x.
## It use stochastic gradient algorithm obviously.
## For example:
##
## @example
## @group
## x=[1 4;2 5;5 1; 4 2] y = [ 19 26 19 20]
## batch_gradient (x, y)
##   @result{} [0.0060406   2.9990063   3.9990063]
## @end group
## @end example
## @seealso{batch_gradient}
## @end deftypefn
## Author: xiuleili <xiuleili@XIULEILI>
## Created: 2013-04-26

function [ theta ] = stochastic_gradient (x,y)
[n,m] = size(x);
[my,ny] = size(y);
if ny!=n | my != 1
error("Error: x should be a matrix with(n,m) and y must be (1,n), where n is the count of training samples.");
end

X = [ones(n,1) x]';
theta = rand(1, m+1);
learning_rate = 0.01;
errors = 1;
threshold=0.000001;
times = 0;
start_time = clock ();
while errors > threshold
for k=[1:n]
xx = X(:,k);
theta += learning_rate * (y(k)-theta*xx)*xx';
end
errors = sum((y-theta*X).^2);
times ++;
printf("[%d] errors = %f", times, errors);
disp(theta);
if(times > 10000000000)
break;
end
end
end_time = clock ();
disp( seconds(end_time - start_time));
endfunction

备注

seconds是一自定义函数：

## seconds

## Author: xiuleili <xiuleili@XIULEILI>
## Created: 2013-04-26

function [ ret ] = seconds (t)
t=round(t);
ret = t(6) + t(5)*60 + t(4)*3600+t(3)*3600*24;
endfunction

考参:

[1]易网公开课, 机器学习 http://v.163.com/special/opencourse/machinelearning.html
[2]C++实现 http://blog.sina.com.cn/s/blog_69821363010156rs.html
文章结束给大家分享下程序员的一些笑话语录：

Bphone之你们聊，我先走了！移动说：我在phone前加o，我叫o缝；苹果说：我在phone前i，我是i缝；微软说：我在phone前加w，我叫w缝；三星说：你们聊，我先走了！

将来王建宙写回忆录的时候，一定要有一句“常小兵为中国移动的发展做出了不可磨灭的贡献”。