粗糙集约简算法的实现（代码）

function [F,M]=MI_mRMR(data,FC,delta) %%%%ranking features with mRMR and mutual information %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % rank features based on mutual information and minimal redundancy and % maximal revelance (mRMR) strategy. % Note: mutual information in this algorithm is not the classical one. If % features are categorical, MI is derived from Shannon's entropy. However, % if features are numerical, MI becomes Neighborhood Mutual information or % Fuzzy mutual information dependent on parameter "FC" % Detailed information about mRMR, please refer to Hanchuan Peng, Fuhui Long, Chris Ding. Feature Selection Based on Mutual Information: Criteria of Max-Dependency, Max-Relevance, and Min-Redundancy. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 8, AUGUST 2005. % F is the ranking of features % M is the corresponding significance of features % FC is to set the fuzzy(F) or crisp(C) mutual information % delta is the size of neighborhood % Shuang An, Qinghua Hu Oct. 2008, Harbin Institute of Technology % http://www.turbo.hit.edu.cn/members/huqinghua [row,column]=size(data); %%%%%%%%%%%%%compute the relation matrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:column col=i; r=[]; eval(['ssr' num2str(col) '=[];']); for j=1:row a=data(j,col); x=data(:,col); if (FC=='F') for m=1:length(x) r(j,m)=kersim(a,x(m),deta); end elseif (FC=='C') for m=1:length(x) r(j,m)=kersim_crisp(a,x(m),deta); end end end eval(['ssr' num2str(col) '=r;']); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M=[]; % Save the significance of features a=[]; % Save the ranking of features attri=ones(1,column-1); m=0; t=1; %%%%%%%%%%%%%%%Select the first features%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:column-1 r1=eval(['ssr' num2str(i)]); r2=eval(['ssr' num2str(column)]); P=mutuinfo1(r1,r2); if(P>m) m=P; t=i; end a(1)=t; M(1)=m; end attri(t)=0; %如果该特征被选中则将该特征在原数据集中的序号置0；当选择下一个特征时则跳过该特征 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=2:column-2 %Select the 2nd, 3rd,...features m=-1; for k=1:column-1 if (attri(k)==1) r1=eval(['ssr' num2str(k)]); r2=eval(['ssr' num2str(column)]); P1=mutuinfo1(r1,r2); %mutual between features and decision P2=0; for j=1:i-1 r1=eval(['ssr' num2str(k)]); r2=eval(['ssr' num2str(a(j))]); K=mutuinfo1(r1,r2); P2=P2+K; end P2=P2/(i-1); % the average mutual information between features P=P1-P2; % the significance of features if(P>m) m=P; %save the maximal P t=k; end end end a(i)=t; M(i)=m; attri(t)=0; end for i=1:column-1 %the last feature if (attri(i)==1) a=[a i]; end end %%%%% compute fuzzy mutual information %%%%%%%%%%%%%%%%%%%%%%%%%%%% function S=mutuinfo1(M1,M2) S1=entropy(M1); S2=entropy(M2); S3=fs_jointentropy(M1,M2); S=S1+S2-S3; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% compute fuzzy information entropy%%%%%%%%%%%%%%%%%%%%%%%%%%%% function s=entropy(M) [a,b]=size(M); K=0; for i=1:a S(i)=-(1/a)*log2(sum(M(i,:))/a); end s=sum(S); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%compute fuzzy binary relation%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function kersim=kersim(a,x,e) if abs(a-x)>e kersim=0; else if (e==0) if (a==x) kersim=1; else kersim=0; end else kersim=1-abs(a-x)/e; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%compute crisp binary relation%%%%%%%%%%%%%%%%%%%% function kersim=kersim_crisp(a,x,e) if abs(a-x)>e kersim=0; else kersim=1; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%compute fuzzy joint information entropy %%%%%%%%%%%%%%%%%%%%%%% function [S]=fs_jointentropy(M1,M2) [a,b]=size(M1); K=0; for i=1:a Si=-(1/a)*log2(sum(min(M1(i,:),M2(i,:)))/a); K=K+Si; Si=0; end S=K; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%