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Version 1
只能针对离散型输入属性，和预测Label为二分类的情况
——2017.11.4
主函数

size_kvs=size(key_value);
label_class=map_reduce(label);

positive_num=label_class(2,2);
negative_num=label_class(1,2);
entropy=Entropy(size_kvs(1),positive_num,negative_num);
ID3=zeros(size_kvs(2),1);

for id=1:size_kvs(2)
    kv=key_value(:,id);
    KVS=map_reduce(kv);
    positive_kv=[];
    negative_kv=[];
    for i=1:size_kvs(1)
        if label(i)==label_class(2,1)
            positive_kv=[positive_kv;kv(i)];
        elseif label(i)==label_class(1,1)
            negative_kv=[negative_kv;kv(i)];
        end
    end
    positive_KVS=map_reduce(positive_kv);
    negative_KVS=map_reduce(negative_kv);

    entropy_conditional=Entropy_Conditional(KVS,size_kvs(1),positive_KVS,negative_KVS);
    % 计算联合熵
    ID3(id)=entropy-entropy_conditional;
end
% 选择最大的联合熵的属性id
[value,id]=max(ID3)

伪map_reduce函数

function KVS=map_reduce(k_v)
    input=k_v;
    unique_input=unique(k_v,'rows');
    count=histc(input,unique_input);
    KVS=[unique_input,count];
end

计算熵值

function entropy=Entropy(num,num_p,num_n)
    entropy=0;
    p1=(-num_p/num);
    p2=(-num_n/num);
    if p1==0
        entropy=entropy+0;
    else
        entropy=entropy+p1*log2(num_p/num);
    end
        
    if p2==0
        entropy=entropy+0;
    else
        entropy=entropy+(-num_n/num)*log2(num_n/num);
    end
    
end

计算条件熵

function entropy=Entropy_Conditional(KVS,num,p_KVS,n_KVS)
    size_KVS=size(KVS);
    size_p=size(p_KVS);
    size_n=size(n_KVS);
    c_entropy=zeros(size_KVS(1),2);
    for i=1:size_KVS(1)
        for j=1:size_p(1)
            if KVS(i,1)==p_KVS(j,1)
                c_entropy(i,1)=p_KVS(j,2);
            end
        end
    end
    
    for i=1:size_KVS(1)
        for j=1:size_n(1)
            if KVS(i,1)==n_KVS(j,1)
                c_entropy(i,2)=n_KVS(j,2);
            end
        end
    end
    
    c_entropy=[KVS,c_entropy];
    
    pc=0;
    for i=1:size_KVS(1)
        e=Entropy(c_entropy(i,2),c_entropy(i,3),c_entropy(i,4));
        pc=pc+(c_entropy(i,2)/num)*e;
    end
    
    entropy=pc;
end