Hierarchical cluster算法介绍

　　突然想记录几个聚类算法，由于实力有限就先介绍一下层次聚类算法(Hierarchical cluster algorithm),这个聚类算法思想简单，但实现起来感觉复杂度挺大；以前看过《集体智慧编程》里介绍过，里面是用python实现的，由于python里面的列表和字典用起来方便，故实现该算法还行；这里我用c++重新写了一下，感觉代码蛮臃肿，可能是自己的c++没有学习好吧！！！对于容器的使用还不够熟练，这里贴出来的目的是希望哪位大牛看到了指导一二，这里感激不尽。废话不多说了，进入正题吧！

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Hierarchical cluster Algorithm的大致介绍

　　层次聚类算法有两种实现思想，一种是初始时将每个待聚类的数据样本视为一个cluster,采用合并的方式，每次合并两个"距离"最近的cluster，直到合并成一个cluster为止(当然可以在达到自己设定想得到的cluster个数时终止迭代)；另一种刚好与第一种相反，初始时将所有的数据样本视为一个cluster,采用分解的方式(这里没有实现就不说太多)。

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算法的步骤及相关问题

　　算法步骤:  (1)初始时，将每个数据样本视为一个cluster(选取一个度量两个cluster距离的方式)，

　　　　　　　(2)计算任意两个cluster之间的距离；每次选取距离最小的两个cluster，

　　　　　　　(3)合并(2)中选择的两个cluster,将合并产生的新cluster加入cluster set中，并删除被合并的两个cluster，

　　　　　　　(4)重复(2)(3)，知道cluster set中元素只剩下一个为止。

　　相关问题: (1)度量两个cluster之间的距离，应该选择哪种距离？？？《集体智慧编程》中选择的是Pearson,当然也可以直接选用欧氏距离

　　　　　　  (2)如何合并两个cluster,即新的cluster对应的属性值如何表示???这里是用被合并的两个cluster的平均值表示新的cluster

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 /**
 ** Hierarchical cluster Algorithm
 ** step：(1)Firstly,regard each sample as a cluster, and
          (2)Each time merge two clusters if the distance between them is lowest.
          (3)then add the new cluster into cluster set, and delete two clusters merged from cluster set.
 ** method: (1)as to merging, here replace the old two clusters with their average;
            (2)measure the distance with the Pearson similarity.
 ** Time：2013/7/10
 **/
 #include <iostream>
 #include <map>
 #include <vector>
 #include <string>
 #include <fstream>
 #include <cstring>
 #include <sstream>
 #include <cmath>
 #include <iterator>
 using namespace std;
 //cluster
 typedef    struct bicluster{
     vector<double> attri;//attribute
     int  cid;//cluster id
 }Bicluster;
 //a pair
 typedef struct lowpair{
     int leftid;
     int rightid;
     double dist;
 }Lpair;

 /*****************************************************************
 ** convert string(char*) to double(or other type)
 ** here should be included <sstream> before using the stringstream
 ******************************************************************/
 double str2double(char* str){
     stringstream ss;
     ss << str;
     double tmp;
     ss >> tmp;
     return tmp;
 }
 /*****************************************************************
 ** split the string containing some special tokens
 ******************************************************************/
 string split(string &str, vector<double>& dvec, const char* tok){
     char *pch = NULL;
     pch = strtok(const_cast<char*>(str.c_str()), tok);
     string stmp(pch);
     while( pch != NULL ){
         pch = strtok(NULL, tok);
         if( !pch )
             break;
         dvec.push_back(str2double(pch));
     }
     return stmp;
 }
 /******************************************************************
 ** read data from 'blogdata.txt'
 ** @is ------- a reference to ifstream object(input)
 ** @data ----- a map used to store the data (output)
 ******************************************************************/
 bool readfile(ifstream &is, map<string, vector<double> >& mydata){
     if( is.fail() ){
         cerr << "can't open the file !!!" << endl;
         return false;
     }
     //ignore the first line of file
     string str;
     getline(is, str);

     //store the data read from file into mydata
     while( !is.eof() ){
         vector<double> dtmp;
         string tmp;
         getline(is, str);
         tmp = split(str, dtmp, "\t");
         mydata.insert(pair<string,vector<double> >(tmp, dtmp));
     }
     return true;
 }
 /*****************************************************************
 ** compute the distance between two clusters
 ** Note that Pearson value devotes to the similarity between
     two clusters, that is, the greater the Pearson value, the
     lower the distance between them.
 *****************************************************************/
 double distPearson(vector<double>& left, vector<double>& right){
     double sum1 = ;
     double sum2 = ;
     int len = left.size();
     for(int i=; i<len; ++i){
         sum1 += left[i];
         sum2 += right[i];
     }

     /**
     ** maybe you will feel it's complex,
     **  and here we could replace Pearson with Euclidean distance
     **/
     double sum1Sq = ;
     double sum2Sq = ;
     for(int j=; j<len; ++j){
         sum1Sq += pow(left[j], );
         sum2Sq += pow(right[j], );
     }

     double pSum = , num, den;
     for(int k=; k<len; ++k)
         pSum += left[k]*right[k];
     num = pSum - sum1*sum2 / len;
     den = sqrt((sum1Sq - pow(sum1,)/len) * (sum1Sq - pow(sum2,)/len));
     if( den ==  )
         return ;
     return 1.0 - num/den;
 }
 /*************************************************************
 ** Given two clusters, the distance between them
     should be checked whether it exists before compute it.
 **************************************************************/
 bool isExist(vector<Lpair> &lp, int leftid, int rightid, double &d){
     vector<Lpair>::iterator it = lp.begin();
     for(; it!=lp.end(); ++it){
         if( (it->leftid==leftid) && (it->rightid==rightid) ){
             d = it->dist;//if the distance has been computed, assign its value to d
             return true;
         }
     }
     d = ;
     return false;
 }
 /*************************************************************
 ** Given a cluster's id, delete the cluster from cluster set
 **************************************************************/
 void Del(vector<Bicluster> &cvec, int clusterid){
     vector<Bicluster>::iterator it = cvec.begin();
     for(; it!=cvec.end(); ++it){
         if( it->cid == clusterid )
             break;
     }
     cvec.erase(it);
 }
 /*************************************************************
 ** Hierarchical Cluster Algorithm
 **************************************************************/
 void HierarchicalCluster(map<string, vector<double> > &mydata){
     vector<Lpair> distances;//used to store the distance

     //firstly,regard each sample as a cluster
     vector<Bicluster> cvec;
     map<string, vector<double> >::iterator it = mydata.begin();
     int myid = ;
     for(; it!= mydata.end(); ++it){
         Bicluster btmp;
         btmp.attri = it->second;
         btmp.cid = myid++;
         cvec.push_back(btmp);
     }
     myid = -;
     //search the pair
     while( cvec.size()> ){
         Lpair lowp;
         double closedis = distPearson(cvec[].attri,cvec[].attri);
         lowp.leftid = cvec[].cid, lowp.rightid = cvec[].cid;
         lowp.dist = closedis;

         int leftps = , rightps = ;
         for(int ix=; ix<cvec.size(); ++ix){
             for(int iy=ix+; iy<cvec.size(); ++iy){
                 double d;
                 int lid = cvec[ix].cid, rid = cvec[iy].cid;
                 if( !isExist(distances,lid,rid,d) ){
                     Lpair lptmp;
                     lptmp.dist = distPearson(cvec[ix].attri, cvec[iy].attri);
                     lptmp.leftid = lid;
                     lptmp.rightid= rid;
                     distances.push_back(lptmp);
                     d = lptmp.dist;
                   }
                  if( d < lowp.dist ){
                      lowp.leftid = lid;
                      lowp.rightid = rid;
                      leftps = ix;
                      rightps = iy;
                      lowp.dist = d;
                  }
             }
         }
         //create a new cluster
         Bicluster ncluster;
         for(int i=; i<cvec[].attri.size(); ++i){
             double av;
             av = (cvec[leftps].attri[i] + cvec[rightps].attri[i]) / 2.0;
             ncluster.attri.push_back(av);
         }
         ncluster.cid = myid--;//assign negative to the new cluster's id
         cout << "leftid: " << lowp.leftid <<  ", rightid: " << lowp.rightid << endl;
         //delete the pair
         Del(cvec, lowp.leftid);
         Del(cvec, lowp.rightid);
         cvec.push_back(ncluster);
     }
 }
 int main()
 {
     ifstream is("blogdata.txt");
     if( is.fail() ){
         cerr << "error!!!" << endl;
         exit(-);
     }
     map<string, vector<double> > mydata;
     if(readfile(is, mydata))
         HierarchicalCluster(mydata);
     return ;
 }

　　代码写的有点乱且复杂，最后显示的结果不是树状图（python很易实现），只是简单的显示了每次被合并的两个cluster的id.代码中用到的数据可以从http://kiwitobes.com/clusters/blog.txt下载得到。