决策树ID3源程序

1、id3算法的matlab实现转帖functionD=ID3(train_features,train_targets,params,region)functiontargets=use_tree(features,indices,tree,Nbins,Uc)%Classifyrecursivelyusingatreetargets=zeros(1,size(features,2);if(size(features,1)=1),%Onlyonedimensionleft,soworkonitfori=1:Nbins,in=indices(find(features(indices)=i);ifi

2、sempty(in),ifisfinite(tree.child(i),targets(in)=tree.child(i);else%Nodatawasfoundinthetrainingsetforthisbin,sochooseitrandomallyn=1+floor(rand(1)*length(Uc);targets(in)=Uc(n);endendendbreakend%Thisisnotthelastlevelofthetree,so:%First,findthedimensionwearetoworkondim=tree.split_dim;dims=find(ismember

3、(1:size(features,1),dim);%Andclassifyaccordingtoitfori=1:Nbins,in=indices(find(features(dim,indices)=i);targets=targets+use_tree(features(dims,:),in,tree.child(i),Nbins,Uc);end%ENDuse_treefunctiontree=make_tree(features,targets,inc_node,Nbins)%BuildatreerecursivelyNi,L=size(features);Uc=unique(targe

4、ts);%Whentostop:Ifthedimensionisoneorthenumberofexamplesissmallif(Ni=1)|(inc_nodeL),%Computethechildrennon-recursivelyfori=1:Nbins,tree.split_dim=0;indices=find(features=i);ifisempty(indices),if(length(unique(targets(indices)=1),tree.child(i)=targets(indices(1);elseH=hist(targets(indices),Uc);m,T=ma

5、x(H);tree.child(i)=Uc(T);endelsetree.child(i)=inf;endendbreakend%ComputethenodesIfori=1:Ni,Pnode(i)=length(find(targets=Uc(i)/L;endInode=-sum(Pnode.*log(Pnode)/log(2);%Foreachdimension,computethegainratioimpuritydelta_Ib=zeros(1,Ni);P=zeros(length(Uc),Nbins);fori=1:Ni,forj=1:length(Uc),fork=1:Nbins,

6、indices=find(targets=Uc(j)&(features(i,:)=k)P(j,k)=length(indices);endendPk=sum(P);P=P/L;Pk=Pk/sum(Pk);info=sum(-P.*log(eps+P)/log(2);delta_Ib(i)=(Inode-sum(Pk.*info)/-sum(Pk.*log(eps+Pk)/log(2);end%Findthedimensionminimizingdelta_Ibm,dim=max(delta_Ib);%Splitalongthedimdimensiontree.split_dim=dim;di

7、ms=find(ismember(1:Ni,dim);fori=1:Nbins,indices=find(features(dim,:)=i);tree.child(i)=make_tree(features(dims,indices),targets(indices),inc_node,Nbins);endC4.5functionD=C4_5(train_features,train_targets,inc_node,region)%ClassifyusingQuinlansC4.5algorithm%Inputs:%features-Trainfeatures%targets-Traint

8、argets%inc_node-Percentageofincorrectlyassignedsamplesatanode%region-Decisionregionvector:-xx-yynumber_of_points%Outputs%D-Decisionsufrace%NOTE:Inthisimplementationitisassumedthatafeaturevectorwithfewerthan10uniquevalues(theparameterNu)%isdiscrete,andwillbetreatedassuch.Othervectorswillbetreatedasco

9、ntinuousNi,M=size(train_features);inc_node=inc_node*M/100;Nu=10;%ForthedecisionregionN=region(5);mx=ones(N,1)*linspace(region(1),region(2),N);my=linspace(region(3),region(4),N)*ones(1,N);flatxy=mx(:),my(:);%Preprocessing%f,t,UW,m=PCA(train_features,train_targets,Ni,region);%train_features=UW*(train_

10、features-m*ones(1,M);%flatxy=UW*(flatxy-m*ones(1,NA2);%Findwhichoftheinputfeaturesarediscrete,anddiscretisizethecorresponding%dimensiononthedecisionregiondiscrete_dim=zeros(1,Ni);fori=1:Ni,Nb=length(unique(train_features(i,:);if(Nb=Nu),%Thisisadiscretefeaturediscrete_dim(i)=Nb;H,flatxy(i,:)=high_his

11、togram(flatxy(i,:),Nb);endend%Buildthetreerecursivelydisp(Buildingtree)tree=make_tree(train_features,train_targets,inc_node,discrete_dim,max(discrete_dim),0);%Makethedecisionregionaccordingtothetreedisp(Buildingdecisionsurfaceusingthetree)targets=use_tree(flatxy,1:NA2,tree,discrete_dim,unique(train_

12、targets);D=reshape(targets,N,N);%ENDfunctiontargets=use_tree(features,indices,tree,discrete_dim,Uc)%Classifyrecursivelyusingatreetargets=zeros(1,size(features,2);if(tree.dim=0)%Reachedtheendofthetreetargets(indices)=tree.child;breakend%Thisisnotthelastlevelofthetree,so:%First,findthedimensionweareto

13、workondim=tree.dim;dims=1:size(features,1);%Andclassifyaccordingtoitif(discrete_dim(dim)=0),%Continuousfeaturein=indices(find(features(dim,indices)tree.split_loc);targets=targets+use_tree(features(dims,:),in,tree.child(2),discrete_dim(dims),Uc);else%DiscretefeatureUf=unique(features(dim,:);fori=1:le

14、ngth(Uf),in=indices(find(features(dim,indices)=Uf(i);targets=targets+use_tree(features(dims,:),in,tree.child(i),discrete_dim(dims),Uc);endend%ENDuse_treefunctiontree=make_tree(features,targets,inc_node,discrete_dim,maxNbin,base)%BuildatreerecursivelyNi,L=size(features);Uc=unique(targets);tree.dim=0;

15、%tree.child(1:maxNbin)=zeros(1,maxNbin);tree.split_loc=inf;ifisempty(features),breakend%Whentostop:Ifthedimensionisoneorthenumberofexamplesissmallif(inc_nodeL)|(L=1)|(length(Uc)=1),H=hist(targets,length(Uc);m,largest=max(H);tree.child=Uc(largest);breakend%ComputethenodesIfori=1:length(Uc),Pnode(i)=l

16、ength(find(targets=Uc(i)/L;endInode=-sum(Pnode.*log(Pnode)/log(2);%Foreachdimension,computethegainratioimpurity%Thisisdoneseparatelyfordiscreteandcontinuousfeaturesdelta_Ib=zeros(1,Ni);split_loc=ones(1,Ni)*inf;fori=1:Ni,data=features(i,:);Nbins=length(unique(data);if(discrete_dim(i),%Thisisadiscrete

17、featureP=zeros(length(Uc),Nbins);forj=1:length(Uc),fork=1:Nbins,indices=find(targets=Uc(j)&(features(i,:)=k);P(j,k)=length(indices);endendPk=sum(P);P=P/L;Pk=Pk/sum(Pk);info=sum(-P.*log(eps+P)/log(2);delta_Ib(i)=(Inode-sum(Pk.*info)/-sum(Pk.*log(eps+Pk)/log(2);else%ThisisacontinuousfeatureP=zeros(len

18、gth(Uc),2);%Sortthefeaturessorted_data,indices=sort(data);sorted_targets=targets(indices);%CalculatetheinformationforeachpossiblesplitI=zeros(1,L-1);forj=1:L-1,fork=1:length(Uc),P(k,1)=length(find(sorted_targets(1:j)=Uc(k);P(k,2)=length(find(sorted_targets(j+1:end)=Uc(k);endPs=sum(P)/L;P=P/L;info=sum(-P.*log(eps+P)/log(2);I(j)=Inode-sum(info.*Ps);enddelta_Ib(i),s=max(I);split_loc(i)=sorted_data(s);endend%Findthedimensionminimizingdelt