标签：trim lap ber error ted i+1 title 组成 doc
广义上来说，任何在算法中用到SVD/特征值分解的，都叫Spectral Algorithm。顺便说一下，对于任意矩阵只存在奇异值分解，不存在特征值分解。对于正定的对称矩阵，奇异值就是特征值，奇异向量就是特征向量。
传统的聚类算法，如K-Means、EM算法都是建立在凸球形样本空间上，当样本空间不为凸时，算法会陷入局部最优，最终结果受初始参数的选择影响比较大。而谱聚类可以在任意形状的样本空间上聚类，且收敛于全局最优解。
谱聚类和CHAMELEON聚类很像，都是把样本点的相似度放到一个带权无向图中，采用“图划分”的方法进行聚类。只是谱聚类算法在进行图划分的时候发现计算量很大，转而求特征值去了，而且最后还在几个小特征向量组成的矩阵上进行了K-Means聚类。
Simply speaking，谱聚类算法分为3步：
从文件读入样本点，最终算得矩阵L
#include<math.h>#include<string.h>#include"matrix.h"#include"svd.h"#define N 19 //样本点个数#define K 4 //K-Means算法中的K#define T 0.1 //样本点之间相似度的阈值double sample[N][2]; //存放所有样本点的坐标（2维的）void readSample(char *filename){ FILE *fp; if((fp=fopen(filename,"r"))==NULL){ perror("fopen"); exit(0); } char buf[50]={0}; int i=0; while(fgets(buf,sizeof(buf),fp)!=NULL){ char *w=strtok(buf," \t"); double x=atof(w); w=strtok(NULL," \t"); double y=atof(w); sample[i][0]=x; sample[i][1]=y; i++; memset(buf,0x00,sizeof(buf)); } assert(i==N); fclose(fp);}double** getSimMatrix(){ //为二维矩阵申请空间 double **matrix=getMatrix(N,N); //计算样本点两两之间的相似度，得到矩阵W int i,j; for(i=0;i<N;i++){ matrix[i][i]=1; for(j=i+1;j<N;j++){ double dist=sqrt(pow(sample[i][0]-sample[j][0],2)+pow(sample[i][1]-sample[j][1],2)); double sim=1.0/(1+dist); if(sim>T){ matrix[j][i]=sim; matrix[i][j]=sim; } } } //计算L=D-W for(j=0;j<N;j++){ double sum=0; for(i=0;i<N;i++){ sum+=matrix[i][j]; if(i!=j) matrix[i][j]=0-matrix[i][j]; } matrix[j][j]=matrix[j][j]-sum; } return matrix;}int main(){ char *file="/home/orisun/data"; readSample(file); double **L=getSimMatrix(); printMatrix(L,N,N); double **M=singleVector(L,N,N,5); printMatrix(M,N,5); freeMatrix(L,N); return 0;} |
L已是对称矩阵，直接奇异值分解的得到的就是特征向量
最后是运行KMeans的Java代码
package ai;public class Global { //计算两个向量的欧氏距离 public static double calEuraDist(double[] arr1,double[] arr2,int len){ double result=0.0; for(int i=0;i<len;i++){ result+=Math.pow(arr1[i]-arr2[i],2.0); } return Math.sqrt(result); }} |
package ai;public class DataObject { String docname; double[] vector; int cid; boolean visited; public DataObject(int len){ vector=new double[len]; } public String getName() { return docname; } public void setName(String docname) { this.docname = docname; } public double[] getVector() { return vector; } public void setVector(double[] vector) { this.vector = vector; } public int getCid() { return cid; } public void setCid(int cid) { this.cid = cid; } public boolean isVisited() { return visited; } public void setVisited(boolean visited) { this.visited = visited; }} |
package ai;import java.io.BufferedReader;import java.io.File;import java.io.FileReader;import java.io.IOException;import java.util.ArrayList;import java.util.Iterator;public class DataSource { ArrayList<DataObject> objects; int row; int col; public void readMatrix(File dataFile) { try { FileReader fr = new FileReader(dataFile); BufferedReader br = new BufferedReader(fr); String line = br.readLine(); String[] words = line.split("\\s+"); row = Integer.parseInt(words[0]); // row=1000; col = Integer.parseInt(words[1]); objects = new ArrayList<DataObject>(row); for (int i = 0; i < row; i++) { DataObject object = new DataObject(col); line = br.readLine(); words = line.split("\\s+"); for (int j = 0; j < col; j++) { object.getVector()[j] = Double.parseDouble(words[j]); } objects.add(object); } br.close(); } catch (IOException e) { e.printStackTrace(); } } public void readRLabel(File file) { try { FileReader fr = new FileReader(file); BufferedReader br = new BufferedReader(fr); String line = null; for (int i = 0; i < row; i++) { line = br.readLine(); objects.get(i).setName(line.trim()); } } catch (IOException e) { e.printStackTrace(); } } public void printResult(ArrayList<DataObject> objects, int n) { //DBScan是从第1类开始，K-Means是从第0类开始// for (int i =0; i <n; i++) { for(int i=1;i<=n;i++){ System.out.println("=============属于第"+i+"类的有：==========================="); Iterator<DataObject> iter = objects.iterator(); while (iter.hasNext()) { DataObject object = iter.next(); int cid=object.getCid(); if(cid==i){ System.out.println(object.getName());// switch(Integer.parseInt(object.getName())/1000){// case 0:// System.out.println(0);// break;// case 1:// System.out.println(1);// break;// case 2:// System.out.println(2);// break;// case 3:// System.out.println(3);// break;// case 4:// System.out.println(4);// break;// case 5:// System.out.println(5);// break;// default:// System.out.println("Go Out");// break;// } } } } }} |
package ai;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 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) { 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")); int len = datasource.col; // 划分为4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。"); }} |
标签：trim lap ber error ted i+1 title 组成 doc
原文地址：https://www.cnblogs.com/lm3306/p/9314032.html
