竞争性自适应重加权

用于matlab模式识别（分类和回归）的特征变量提取方法，竞争性自适应重加权算法（CARS）是通过自适应重加权采样（ARS）技术选择出PLS模型中回归系数绝对值大的波长点，去掉权重小的波长点，利用交互验证选出RMSECV指最低的子集，可有效寻出最优变量组合。

function F=carspls（XyAKmethodnum） 
%+++ CARS: Competitive Adaptive Reweighted Sampling method for variable selection.
%+++ X: The data matrix of size m x p
%+++ y: The reponse vector of size m x 1
%+++ A: the maximal principle to extract.
%+++ K: the group number for cross validation.
%+++ num: the  number of Monte Carlo Sampling runs.
%+++ method: pretreatment method.
%+++ Hongdong Li Dec.15 2008.
%+++ Advisor: Yizeng Liang yizeng_liang@263.net
%+++ lhdcsu@gmail.com
%+++ Ref:  Hongdong Li Yizeng Liang Qingsong Xu Dongsheng Cao Key
%    wavelengths screening using competitive adaptive reweighted sampling 
%    method for multivariate calibration Anal Chim Acta 2009 648（1）:77-84


tic;
%+++ Initial settings.
if nargin<6;num=50;end;
if nargin<5;method=‘center‘;end;
if nargin<4;K=5;end;
if nargin<3;A=2;end;

%+++ Initial settings.
[MxNx]=size（X）;
A=min（[Mx Nx A]）;
index=1:Nx;
ratio=0.9;
r0=1;
r1=2/Nx;
Vsel=1:Nx;
Q=floor（Mx*ratio）;
W=zeros（Nxnum）;
Ratio=zeros（1num）;

%+++ Parameter of exponentially decreasing function. 
b=log（r0/r1）/（num-1）;  a=r0*exp（b）;

%+++ Main Loop
for iter=1:num
     
     perm=randperm（Mx）;   
     Xcal=X（perm（1:Q）:）; ycal=y（perm（1:Q））;   %+++ Monte-Carlo Sampling.
     
     PLS=pls（Xcal（:Vsel）ycalAmethod）;    %+++ PLS model
     w=zeros（Nx1）;coef=PLS.coef_origin（1:end-1end）;
     w（Vsel）=coef;W（:iter）=w; 
     w=abs（w）;                                  %+++ weights
     [wsindexw]=sort（-w）;                      %+++ sort weights
     
     ratio=a*exp（-b*（iter+1））;                      %+++ Ratio of retained variables.
     Ratio（iter）=ratio;
     K=round（Nx*ratio）;  
     
     
     w（indexw（K+1:end））=0;                      %+++ Eliminate some variables with small coefficients.  
     
     Vsel=weightsampling_in（w）;                 %+++ Reweighted Sampling from the pool of retained variables.                 
     Vsel=unique（Vsel）;              
     fprintf（‘The %dth variable sampling finished.\n‘iter）;    %+++ Screen output.
 end

%+++  Cross-Validation to choose an optimal subset;
RMSEP=zeros（1num）;
Q2_max=zeros（1num）;
Rpc=zeros（1num）;
for i=1:num
   vsel=find（W（:i）~=0）;
 
   CV=plscvfold（X（:vsel）yAKmethod0）;  
   RMSEP（i）=CV.RMSECV;
   Q2_max（i）=CV.Q2_max;   
   
   Rpc（i）=CV.optPC;
   fprintf（‘The %d/%dth subset finished.\n‘inum）;
end
[RminindexOPT]=min（RMSEP）;
Q2_max=max（Q2_max）;




%+++ save results;
time=toc;
%+++ output
F.W=W;
F.time=time;
F.cv=RMSEP;
F.Q2_max=Q2_max;
F.minRMSECV=Rmin;
F.iterOPT=indexOPT;
F.optPC=Rpc（indexOPT）;
Ft.ratio=Ratio;
F.vsel=find（W（:indexOPT）~=0）‘;



function sel=weightsampling_in（w）
%Bootstrap sampling
%2007.9.6H.D. Li.

w=w/sum（w）;
N1=length（w）;
min_sec（1）=0; max_sec（1）=w（1）;
for j=2:N1
   max_sec（j）=sum（w（1:j））;
   min_sec（j）=sum（w（1:j-1））;
end
% figure;plot（max_sec‘r‘）;hold on;plot（min_sec）;
      
for i=1:N1
  bb=rand（1）;
  i

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     目录           0  2012-03-23 20:23  CARS_PLS\
     目录           0  2012-03-23 20:23  CARS_PLS\CARS_PLS\
     文件       39936  2012-03-23 20:22  CARS_PLS\CARS_PLS\CARS工具包重要函数.doc
     文件        1332  2012-03-23 20:22  CARS_PLS\CARS_PLS\license.txt
     目录           0  2012-03-23 20:23  CARS_PLS\CARS_PLS\pls\
     文件       49218  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\CARS_manual.pdf
     文件       46264  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\LOGO_CARS.JPG
     文件        1132  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\Manne_bi.m
     文件        3383  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\carspls.m
     文件         920  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\classplot2.m
     文件      448880  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\corn_m51.mat
     文件         288  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\csvd奇异值分解.m
     文件         506  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\example_nir.m
     文件         465  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\expred1.m
     文件         736  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\expred2.m
     文件         812  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\ks.m
     文件         966  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\lsreg.m
     文件        2983  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\mcs.m
     文件        1217  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\mcuvepls.m
     文件         976  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\mwpls.m
     文件        3013  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\oscplscv.m
     文件         835  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plotcars.m
     文件         592  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plotmcs.m
     文件        1953  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\pls.m
     文件        1788  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\pls_nipals.m
     文件        2639  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plscvfold.m
     文件        1955  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plsdcv.m
     文件        2977  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plsmccv.m
     文件        1734  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plsnipals.m
     文件        2179  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plsrdcv.m
     文件        4180  2012-03-23 20:22  CARS_PLS\CARS_PLS\pls\plssim.m
............此处省略10个文件信息