Candidate-Elimination算法是数据挖掘中的一种概念学习算法，部分解决Find-S的不足，可以输出所有与训练样本一致的概念，同时利用概念间偏序关系来指导搜索，其伪代码描述如下
Initialize Gto the set of most-general hypotheses in HInitialize Sto the set of most-specific hypotheses in HFor each training example, d, do:If dis a positive example then:Remove from Gany hypotheses that do not match dFor each hypothesis sin Sthat does not match dRemove sfrom SAdd to S all minimal generalizations, h, of ssuch that:1) h matches d2) some member of Gis more general than hRemove fromSany hthat is more general than another hypothesis in SIf dis a negative example then:Remove from Sany hypotheses that match dFor each hypothesis gin Gthat matches dRemove gfrom GAdd to G all minimal specializations, h, of gsuch that:1) hdoes not match d2) some member of Sis more specific than hRemove fromG any hthat is more specific than another hypothesis in G
花了几个小时的时间总算把这个算法用C++实现测试通过了，采用了STL中的二维Vector容器保存字符串，在调试部分浪费不少时间。主要是用VC++ 6.0查看STL容器中的变量值不太方便，比如Vector，需要在调式窗口里输入s._first,10 才可以看到全部的数据；也可以加输出的测试代码，但是比较麻烦。好了，废话不多说了，贴上代码，希望各位批评指正。
【概念挖掘需求】
基本的算法思想是，泛化边界初始化为全？，特化边界特化为全空集(@),
1、若遇到正实例,首先从G中删除不包含该实例的概念，然后对S删除与实例不相符的概念，同时做最小泛化，使其包含该实例
2、若遇到负实例,首先从S中删除包含了该实例的概念，然后对G删除包含了该实例的概念，同时做最小特化，注意最小特化集是与当前S一一枚举出可能的特化概念，删除那些符合该实例的概念
C++源码
#include <iostream>#include <string>#include <vector>using namespace std;#define MAXLEN 7//输入每行的数据个数//每行为标号 outlook Temperature Humidity Wind PlayTennis Swiming//采用二维动态数组Vector保存处理vector <vector <string> > state;//实例集vector <vector <string> > S;//特化边界vector <vector <string> > G;//泛化边界vector <string> item(MAXLEN);//对应一行实例集string yes("Yes");string all("?");string white("@");//@表示空集string end("end");//输入结束//判定概念h是否包含实例dbool checkInclude(vector <string> h, vector <string> d){bool res = true;for(int i = 1; i < MAXLEN-1; i++){if(!h[i].compare(all) || !h[i].compare(d[i])) continue;else if(!h[i].compare(white) || h[i].compare(d[i])) res = false;else {cerr<<"error in checkInclude"<<endl;res = false;}}return res;}//对概念S[offset]做最小泛化，使得S[offset]包含dvoid doMinGeneral(int offset, vector <string> d){for(int i = 1; i < MAXLEN-1; i++){if(!S[offset][i].compare(white)) {S[offset][i] = d[i];}else if(S[offset][i].compare(d[i])) S[offset][i] = all;else continue;//包括相等和h[i]为all的情况}}//对概念G[offset]做最小特化，使得G[offset]包不含d，注意最小特化来自于和S的组合void doMinSpecific(int offset, vector <string> d, vector <string> s){for(int i = 1; i < MAXLEN-1; i++){if(G[offset][i].compare(s[i]) && !G[offset][i].compare(all)){if(s[i].compare(d[i])){//产生新的泛化边界，注意不唯一vector<string> temp (G[offset]);//先拷贝一份G[offset]temp[i] = s[i];G.push_back(temp);}}if(G[offset][i].compare(s[i]) && G[offset][i].compare(all)){cerr<<"doMinSpecific: error in data"<<endl;//G[offset][i]不为？且其与s[i]不同的情况}}}void input(){int i, j;string s;while(cin>>s,s.compare(end) != 0){//-1为输入结束item[0] = s;for( i = 1;i < MAXLEN; i++){cin>>item[i];}state.push_back(item);}//初始化for( i = 0;i < MAXLEN; i++){item[i] = white;}S.push_back(item);for( i = 0;i < MAXLEN; i++){item[i] = all;}G.push_back(item);}void output(){int i,j;cout<<"The specific boundary is:"<<endl;for(i = 0; i < S.size(); i++){for(j = 1;j < MAXLEN-1; j++){cout<<S[i][j]<<" ";}cout<<endl;}cout<<endl;cout<<"The general boundary is:"<<endl;for(i = 0; i < G.size(); i++){for(j = 1;j < MAXLEN-1; j++){cout<<G[i][j]<<" ";}cout<<endl;}cout<<endl;}void solve(){int i,j;for( i = 0; i < state.size(); i++){if(!state[i][MAXLEN-1].compare(yes)){//正实例的情况,首先从G中删除不包含该实例的概念，//然后对S删除与实例不相符的概念，同时做最小泛化，使其包含该实例for(j = 0; j < G.size(); j++){if(!checkInclude(G[j],state[i])) {G.erase(G.begin() + j);}}for(j = 0; j < S.size(); j++){doMinGeneral(j,state[i]);}}else {//负实例的情况,首先从S中删除包含了该实例的概念， //然后对G做最小特化，与当前S一一枚举出可能的特化概念，删除那些符合该实例的概念for(j = 0; j < S.size(); j++){if(checkInclude(S[j],state[i])){S.erase(S.begin() + j);}}int orginGSize = G.size();//先记下G原始大小for(j = 0; j < orginGSize; j++){doMinSpecific(j,state[i],S[0]);}G.erase(G.begin(), G.begin() + (orginGSize));//删除G[0]到G[orginGSize-1],但是要注意括号内的参数不同}}}int main(){input();solve();output();return 0;}
测试数据一
0 zjdppx Warm High Strong Warm Yes1 zjdppx Warm Normal Strong Warm No2 Rainy Cold High Strong Warm No3 zjdppx Warm High Strong Cool Yesend
测试结果一
The specific boundary is:zjdppx Warm High Strong ?The general boundary is:zjdppx ? High ? ?? Warm High ? ?
测试数据二
0 zjdppx Warm High Strong Warm Yes1 zjdppx Warm Normal Strong Warm No2 Rainy Cold High Strong Warm No3 zjdppx Warm High Strong Cool Yesend测试结果二
The specific boundary is:zjdppx Warm High Strong ?The general boundary is:zjdppx ? High ? ?? Warm High ? ?
具体预测的方法是
1、如果给定的实例符合概念集合S，则一定去游泳
2、如果给定的实例不符合概念集合G，则一定不去游泳
3、如果给定的实例不符合概念集合S，但是符合概念集合G，则可能去游泳