K-means聚类算法原理和C++实现

  1 #include<iostream>
  2 #include<cmath>
  3 #include<vector>
  4 #include<ctime>
  5 using namespace std;
  6 typedef unsigned int uint;
  7 
  8 struct Cluster
  9 {
 10     vector<double> centroid;
 11     vector<uint> samples;
 12 };
 13 double cal_distance(vector<double> a, vector<double> b)
 14 {
 15     uint da = a.size();
 16     uint db = b.size();
 17     if (da != db) cerr << "Dimensions of two vectors must be same!!\n";
 18     double val = 0.0;
 19     for (uint i = 0; i < da; i++)
 20     {
 21         val += pow((a[i] - b[i]), 2);
 22     }
 23     return pow(val, 0.5);
 24 }
 25 vector<Cluster> k_means(vector<vector<double> > trainX, uint k, uint maxepoches)
 26 {
 27     const uint row_num = trainX.size();
 28     const uint col_num = trainX[0].size();
 29 
 30     /*初始化聚类中心*/
 31     vector<Cluster> clusters(k);
 32     uint seed = (uint)time(NULL); 33     for (uint i = 0; i < k; i++)
 34     {
 35         srand(seed);
 36         int c = rand() % row_num;
 37         clusters[i].centroid = trainX[c];
 38         seed = rand();
 39     }
 40 
 41     /*多次迭代直至收敛，本次试验迭代100次*/
 42     for (uint it = 0; it < maxepoches; it++)
 43     {
 44         /*每一次重新计算样本点所属类别之前，清空原来样本点信息*/
 45         for (uint i = 0; i < k; i++)
 46         {
 47             clusters[i].samples.clear();
 48         }
 49         /*求出每个样本点距应该属于哪一个聚类*/
 50         for (uint j = 0; j < row_num; j++)
 51         {
 52             /*都初始化属于第0个聚类*/    
 53             uint c = 0;
 54             double min_distance = cal_distance(trainX[j],clusters[c].centroid);
 55             for (uint i = 1; i < k; i++)
 56             {
 57                 double distance = cal_distance(trainX[j], clusters[i].centroid);
 58                 if (distance < min_distance)
 59                 {
 60                     min_distance = distance;
 61                     c = i;
 62                 }
 63             }
 64             clusters[c].samples.push_back(j);
 65         }
 66 
 67         /*更新聚类中心*/
 68         for (uint i = 0; i < k; i++)
 69         {
 70             vector<double> val(col_num, 0.0); 
 71             for (uint j = 0; j < clusters[i].samples.size(); j++)
 72             {
 73                 uint sample = clusters[i].samples[j];
 74                 for (uint d = 0; d < col_num; d++)
 75                 {
 76                     val[d] += trainX[sample][d];
 77                     if (j == clusters[i].samples.size() - 1)
 78                         clusters[i].centroid[d] = val[d] / clusters[i].samples.size();
 79                 }
 80             }
 81         }
 82     }
 83     return clusters;
 84 }
 85 
 86 int main()
 87 {
 88     vector<vector<double> > trainX(9,vector<double>(1,0));
 89     //对9个数据{1 2 3 11 12 13 21 22 23}聚类
 90     double data = 1.0;
 91     for (uint i = 0; i < 9; i++)
 92     {
 93         trainX[i][0] = data;
 94         if ((i+1) % 3 == 0) data += 8;
 95         else data++;
 96     }
 97 
 98     /*k-means聚类*/
 99     vector<Cluster> clusters_out = k_means(trainX, 3, 100);
100 
101     /*输出分类结果*/
102     for (uint i = 0; i < clusters_out.size(); i++)
103     {
104         cout << "Cluster " << i << " :" << endl; 
105 
106         /*子类中心*/
107         cout << "\t" << "Centroid: " << "\n\t\t[ ";
108         for (uint j = 0; j < clusters_out[i].centroid.size(); j++)
109         {
110             cout << clusters_out[i].centroid[j] << " ";
111         }
112         cout << "]" << endl;
113 
114         /*子类样本点*/
115         cout << "\t" << "Samples:\n";
116         for (uint k = 0; k < clusters_out[i].samples.size(); k++)
117         {
118             uint c = clusters_out[i].samples[k];
119             cout << "\t\t[ ";
120             for (uint m = 0; m < trainX[0].size(); m++)
121             {
122                 cout << trainX[c][m] << " ";
123             }
124             cout << "]\n";
125         }
126     }
127     return 0;
128 }