ada_boost.m

经典教材《机器学习》里的几乎所有算法 作者就是《机器学习》的2大牛人 有的函数添加了中文的注释 仅供参考

function [test_targets, E] = ada_boost(train_patterns, train_targets, test_patterns, params)

% Classify using the AdaBoost algorithm
% Inputs:
% 	train_patterns	- Train patterns
%	train_targets	- Train targets
%   test_patterns   - Test  patterns
%	Params	- [NumberOfIterations, Weak Learner Type, Learner's parameters]
%
% Outputs
%	test_targets	- Predicted targets
%   E               - Errors through the iterations
%
% NOTE: Suitable for only two classes
%


[k_max, weak_learner, alg_param] = process_params(params);%alg_param:weak_learner's 参数

[Ni,M]			= size(train_patterns);
W			 	= ones(1,M)/M;
IterDisp		= 10;

full_patterns   = [train_patterns, test_patterns];
test_targets    = zeros(1, size(test_patterns,2));

%Do the AdaBoosting
for k = 1:k_max,
   %Train weak learner Ck using the data sampled according to W:
   %...so sample the data according to W
   randnum = rand(1,M);%产生M维均匀分布
   cW	   = cumsum(W);%W为权值向量,cW为权向量的累积，考虑概率的定义
   indices = zeros(1,M);
   for i = 1:M,
      %Find which bin the random number falls into,很巧妙的办法来根据W进行抽样
      %桶这样定义，下标i对应的是桶的大小，大小与权值W(i)相关，任取一随机数，显然落在大桶中的概率
      %要大于落在小桶中的概率。这样大桶有更多机会被选中
      loc = max(find(randnum(i) > cW))+1;
      if isempty(loc)
         indices(i) = 1;
      else
         indices(i) = loc;
      end
   end
   
   %...and now train the classifier,此时的测试样本为所有的训练集，这是AdaBoosting的基本做法
   Ck 	= feval(weak_learner, train_patterns(:, indices), train_targets(indices), full_patterns, alg_param);

   %Ek <- Training error of Ck 
   E(k) = sum(W.*(Ck(1:M) ~= train_targets));%这里使用的是传统的二值分类结果
   
   if (E(k) == 0),
      break
   end
   
   %alpha_k <- 1/2*ln(1-Ek)/Ek)%这个公式也有所不同,Ek也类似于论文中的r
   alpha_k = 0.5*log((1-E(k))/E(k));
   
   %W_k+1 = W_k/Z*exp(+/-alpha)
   W  = W.*exp(alpha_k*(xor(Ck(1:M),train_targets)*2-1));
   W  = W./sum(W);
   
   %Update the test targets ,
   %M为训练样本的数目,Ck实际上是所有样本的分类结果，这里当然只取对测试样本的结果并进行累加
   test_targets  = test_targets + alpha_k*(2*Ck(M+1:end)-1);%2*X-1是为了使0,1型变量变成-1,+1型。
   
   if (k/IterDisp == floor(k/IterDisp)),
      disp(['Completed ' num2str(k) ' boosting iterations'])
   end
   
end

test_targets = test_targets > 0;