聚类算法之KMeans(Java实现)

KMeans算法的基本思想是初始随机给定K个簇中心，按照最邻近原则把待分类样本点分到各个簇。然后按平均法重新计算各个簇的质心，从而确定新的簇心。一直迭代，直到簇心的移动距离小于某个给定的值。

当初始簇心选行不好时，KMeans的结果会很差，所以一般是多运行几次，按照一定标准（比如簇内的方差最小化）选择一个比较好的结果。

下图给出对坐标点的聚类结果：

下面给出核心算法的代码：

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/**  * Author: Orisun  * Date: Sep 10, 2011  * FileName: KMeans.java  * Function:  */ package orisun; import java.io.File; import java.util.ArrayList; import java.util.Iterator; import java.util.Random; public class KMeans {     int k; // 指定划分的簇数     double mu; // 迭代终止条件，当各个新质心相对于老质心偏移量小于mu时终止迭代     double[][] center; // 上一次各簇质心的位置     int repeat; // 重复运行次数     double[] crita; // 存放每次运行的满意度     public KMeans(int k, double mu, int repeat, int len) {         this.k = k;         this.mu = mu;         this.repeat = repeat;         center = new double[k][];         for (int i = 0; i < k; i++)             center[i] = new double[len];         crita = new double[repeat];     }     // 初始化k个质心，每个质心是len维的向量，每维均在left--right之间     public void initCenter(int len, ArrayList<DataObject> objects) {         Random random = new Random(System.currentTimeMillis());         int[] count = new int[k]; // 记录每个簇有多少个元素         Iterator<DataObject> iter = objects.iterator();         while (iter.hasNext()) {             DataObject object = iter.next();             int id = random.nextInt(10000)%k;             count[id]++;             for (int i = 0; i < len; i++)                 center[id][i] += object.getVector()[i];         }         for (int i = 0; i < k; i++) {             for (int j = 0; j < len; j++) {                 center[i][j] /= count[i];             }         }     }     // 把数据集中的每个点归到离它最近的那个质心     public void classify(ArrayList<DataObject> objects) {         Iterator<DataObject> iter = objects.iterator();         while (iter.hasNext()) {             DataObject object = iter.next();             double[] vector = object.getVector();             int len = vector.length;             int index = 0;             double neardist = Double.MAX_VALUE;             for (int i = 0; i < k; i++) {                 // double dist = Global.calEuraDist(vector, center[i], len);                 // //使用欧氏距离                 double dist = Global.calEditDist(vector, center[i], len); // 使用编辑距离                 if (dist < neardist) {                     neardist = dist;                     index = i;                 }             }             object.setCid(index);         }     }     // 重新计算每个簇的质心，并判断终止条件是否满足，如果不满足更新各簇的质心,如果满足就返回true.len是数据的维数     public boolean calNewCenter(ArrayList<DataObject> objects, int len) {         boolean end = true;         int[] count = new int[k]; // 记录每个簇有多少个元素         double[][] sum = new double[k][];         for (int i = 0; i < k; i++)             sum[i] = new double[len];         Iterator<DataObject> iter = objects.iterator();         while (iter.hasNext()) {             DataObject object = iter.next();             int id = object.getCid();             count[id]++;             for (int i = 0; i < len; i++)                 sum[id][i] += object.getVector()[i];         }         for (int i = 0; i < k; i++) {             if (count[i] != 0) {                 for (int j = 0; j < len; j++) {                     sum[i][j] /= count[i];                 }             }             // 簇中不包含任何点,及时调整质心             else {                 int a=(i+1)%k;                 int b=(i+3)%k;                 int c=(i+5)%k;                 for (int j = 0; j < len; j++) {                     center[i][j] = (center[a][j]+center[b][j]+center[c][j])/3;                 }             }         }         for (int i = 0; i < k; i++) {             // 只要有一个质心需要移动的距离超过了mu，就返回false             // if (Global.calEuraDist(sum[i], center[i], len) >= mu) { //使用欧氏距离             if (Global.calEditDist(sum[i], center[i], len) >= mu) { // 使用编辑距离                 end = false;                 break;             }         }         if (!end) {             for (int i = 0; i < k; i++) {                 for (int j = 0; j < len; j++)                     center[i][j] = sum[i][j];             }         }         return end;     }     // 计算各簇内数据和方差的加权平均，得出本次聚类的满意度.len是数据的维数     public double getSati(ArrayList<DataObject> objects, int len) {         double satisfy = 0.0;         int[] count = new int[k];         double[] ss = new double[k];         Iterator<DataObject> iter = objects.iterator();         while (iter.hasNext()) {             DataObject object = iter.next();             int id = object.getCid();             count[id]++;             for (int i = 0; i < len; i++)                 ss[id] += Math.pow(object.getVector()[i] - center[id][i], 2.0);         }         for (int i = 0; i < k; i++) {             satisfy += count[i] * ss[i];         }         return satisfy;     }     public double run(int round, DataSource datasource, int len) {         System.out.println("第" + round + "次运行");         initCenter(len,datasource.objects);         classify(datasource.objects);         while (!calNewCenter(datasource.objects, len)) {             classify(datasource.objects);         }         datasource.printResult(datasource.objects, k);         double ss = getSati(datasource.objects, len);         System.out.println("加权方差：" + ss);         return ss;     }     public static void main(String[] args) {         DataSource datasource = new DataSource();         datasource.readMatrix(new File("/home/orisun/test/dot.mat"));         datasource.readRLabel(new File("/home/orisun/test/dot.rlabel")); //      datasource.readMatrix(new File("/home/orisun/text.normalized.mat")); //      datasource.readRLabel(new File("/home/orisun/text.rlabel"));         int len = datasource.col;         // 划分为6个簇，质心移动小于1E-8时终止迭代，重复运行7次         KMeans km = new KMeans(4, 1E-10, 7, len);         int index = 0;         double minsa = Double.MAX_VALUE;         for (int i = 0; i < km.repeat; i++) {             double ss = km.run(i, datasource, len);             if (ss < minsa) {                 minsa = ss;                 index = i;             }         }         System.out.println("最好的结果是第" + index + "次。");     } }