%生成决策树ID3算法
%data:训练集
%feature:属性集
function [node] =createTree(data,feature)type=mostType(data);[m,n]=size(data);%生成节点node%value：分类结果，若为null则表示该节点是分支节点%name:节点划分属性%type:节点属性值%children:子节点node=struct('value','null','name','null','type','null','children',[]);temp_type=data(1,n);temp_b=true;for i=1:mif temp_type!=data(i,n)temp_b=false;endend%样本中全为同一分类结果，则node节点为叶子节点if temp_b==truenode.value=data(1,n);return;end%属性集合为空，将结果标记为样本中最多的分类if sum(feature)==0node.value=type;return;endfeature_bestColumn=bestFeature(data);best_feature=getData()(:,feature_bestColumn);best_distinct=unique(best_feature);best_num=length(best_distinct);best_proc=zeros(best_num,2);best_proc(:,1)=best_distinct(:,1);%循环该属性的每一个值for i=1:best_numDv=[];Dv_index=1;%为node创建一个bach_node分支，设样本data中改属性值为best_proc(i,1)的集合为Dvbach_node=struct('value','null','name','null','type','null','children',[]);for j=1:mif best_proc(i,1)==data(j,feature_bestColumn)Dv(Dv_index,:)=data(j,:);Dv_index=Dv_index+1;endend%Dv为空则将结果标记为样本中最多的分类if length(Dv)==0bach_node.value=type;bach_node.type=best_proc(i,1);bach_node.name=feature_bestColumn;node.children(i)=bach_node;return;elsefeature(feature_bestColumn)=0;%递归调用createTree方法bach_node=createTree(Dv,feature);bach_node.type=best_proc(i,1);bach_node.name=feature_bestColumn;node.children(i)=bach_node;endend
end%获取最优划分属性
function [column] = bestFeature(data)[m,n]=size(data);featureSize=n-1;gain_proc=zeros(featureSize,2);entropy=getEntropy(data);for i=1:featureSizegain_proc(i,1)=i;gain_proc(i,2)=getGain(entropy,data,i);endfor i=1:featureSizeif gain_proc(i,2)==max(gain_proc(:,2))column=i;break;endend
end%计算样本最多的结果
function [res] = mostType(data)[m,n]=size(data);res_distinct = unique(data(:,n));res_proc = zeros(length(res_distinct),2);res_proc(:,1)=res_distinct(:,1);for i=1:length(res_distinct)for j=1:mif res_proc(i,1)==data(j,n)res_proc(i,2)=res_proc(i,2)+1;endendendfor i=1:length(res_distinct)if res_proc(i,2)==max(res_proc(:,2))res=res_proc(i,1);break;endend
end%计算信息熵
function [entropy] = getEntropy(data)entropy=0;[m,n]=size(data);label=data(:,n);label_distinct=unique(label);label_num=length(label_distinct);proc=zeros(label_num,2);proc(:,1)=label_distinct(:,1);for i=1:label_numfor j=1:mif proc(i,1)==data(j,n)proc(i,2)=proc(i,2)+1;endendproc(i,2)=proc(i,2)/m;endfor i=1:label_numentropy=entropy-proc(i,2)*log2(proc(i,2));end
end%计算信息增益
function [gain] = getGain(entropy,data,column)[m,n]=size(data);feature=data(:,column);feature_distinct=unique(feature);feature_num=length(feature_distinct);feature_proc=zeros(feature_num,2);feature_proc(:,1)=feature_distinct(:,1);f_entropy=0;for i=1:feature_numfeature_data=[];feature_proc(:,2)=0;feature_row=1;for j=1:mif feature_proc(i,1)==data(j,column)feature_proc(i,2)=feature_proc(i,2)+1;endif feature_distinct(i,1)==data(j,column)feature_data(feature_row,:)=data(j,:);feature_row=feature_row+1;endendf_entropy=f_entropy+feature_proc(i,2)/m*getEntropy(feature_data);endgain=entropy-f_entropy;