ufldl学习笔记与编程作业：Softmax Regression(vectorization加速)

ufldl出了新教程，感觉比之前的好。从基础讲起。系统清晰，又有编程实践。

在deep learning高质量群里面听一些前辈说，不必深究其它机器学习的算法，能够直接来学dl。

于是近期就開始搞这个了。教程加上matlab编程，就是完美啊。

新教程的地址是：http://ufldl.stanford.edu/tutorial/

本节是对ufldl学习笔记与编程作业：Softmax Regression（softmax回归）版本号的改进。

哈哈，把向量化的写法给写出来了，尼玛好快啊。

仅仅须要2分钟。200迭代就跑完了。

昨晚的for循环写法跑了我1个半小时。

事实上实现向量化写法，要把各种矩阵给在纸上写出来。

1 感谢tornadomeet，尽管他做的是旧教程的实验，可是从他那里学了几个matlab函数。http://www.cnblogs.com/tornadomeet/archive/2013/03/23/2977621.html

比方sparse和full。‘

2 还有从旧教程http://deeplearning.stanford.edu/wiki/index.php/Exercise:Softmax_Regression

学了

% M is the matrix as described in the text
M = bsxfun(@rdivide, M, sum(M))

3 新教程学到了

I=sub2ind(size(A), 1:size(A,1), y);
values = A(I);

下面是softmax_regression_vec.m代码：

function [f,g] = softmax_regression_vec(theta, X,y)
  %
  % Arguments:
  %   theta - A vector containing the parameter values to optimize.
  %       In minFunc, theta is reshaped to a long vector.  So we need to
  %       resize it to an n-by-(num_classes-1) matrix.
  %       Recall that we assume theta(:,num_classes) = 0.
  %
  %   X - The examples stored in a matrix.  
  %       X(i,j) is the i'th coordinate of the j'th example.
  %   y - The label for each example.  y(j) is the j'th example's label.
  %
  m=size(X,2);
  n=size(X,1);

  %theta本来是矩阵，传參的时候，theta(:)这样进来的。是一个vector。仅仅有一列，如今我们得把她变为矩阵
  % theta is a vector;  need to reshape to n x num_classes.
  theta=reshape(theta, n, []);
  num_classes=size(theta,2)+1;
  
  % initialize objective value and gradient.
  f = 0;
  g = zeros(size(theta));

  h = theta'*X;%h(k,i)第k个theta。第i个样本
  a = exp(h);
  a = [a;ones(1,size(a,2))];%加1行
  p = bsxfun(@rdivide,a,sum(a));
  c = log2(p);
  i = sub2ind(size(c), y,[1:size(c,2)]);
  values = c(i);
  f = -sum(values);

  d = full(sparse(1:m,y,1));
  d = d(:,1:(size(d,2)-1));
  p = p(1:(size(p,1)-1),:);%减1行
  g = X*(p'.-d);

  %
  % TODO:  Compute the softmax objective function and gradient using vectorized code.
  %        Store the objective function value in 'f', and the gradient in 'g'.
  %        Before returning g, make sure you form it back into a vector with g=g(:);
  %
%%% YOUR CODE HERE %%%
  
  g=g(:); % make gradient a vector for minFunc

本文作者：linger

本文链接：http://blog.csdn.net/lingerlanlan/article/details/38425929