聚类结果的评估指标及其JAVA实现

一. 前言

又GET了一项技能。在做聚类算法的时候，由于要评估所提出的聚类算法的好坏，于是需要与一些已知的算法对比，或者用一些人工标注的标签来比较，于是用到了聚类结果的评估指标。我了解了以下几项。

首先定义几个量：（借鉴该博客：http://blog.csdn.net/luoleicn/article/details/5350378）

TP:是指被聚在一类的两个量被正确的分类了（即在标准标注里属于一类的两个对象被聚在一类）

TN:是指不应该被聚在一类的两个对象被正确地分开了（即在标准标注里不是一类的两个对象在待测结果也没聚在一类）

FP：指不应该放在一类的对象被错误的放在了一类。（即在标准标注里不是一类，但在待测结果里聚在一类）

FN：指不应该分开的对象被错误的分开了。（即在标准标注里是一类，但在待测结果里没聚在一类）

P = TP + FP

N = TN + FN

1.准确率、识别率：(rank Index)  RI

accuracy = (TP + TN)/(P + N)

2.错误率、误分类率

error rate = (FP + FN)/(P + N)

3.敏感度

sensitivity = TP / P

4.特效性

specificity = TN / N

5.精度

precision = TP  /   (TP + FP)

6.召回率

recall  =  TP  /   (TP  + FN)

7.RI  其实就是  1  的 accuracy

8.F度量

P为precision

R为recall

9.NMI(normalized mutual information)

10 Jaccard

J = TP  / (TP + F)

二、JAVA实现（未优化）

其中很多重复代码，还没有优化。。。

package others;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Set;

import javax.rmi.CORBA.Util;

import org.graphstream.algorithm.measure.NormalizedMutualInformation;


/*function:常用的聚类评价指标有purity, precision, recall，  RI 和 F-score,jaccard
 * @param:
 * @author:Wenbao Li
 * @Data:2015-07-13
 */
public class ClusterEvaluation {

	public static void main(String[] args){
		int[] A = {1,3,3,3,3,3,3,2,1,0,2,0,2,0,2,1,1,0,1,1};
		int[] B = {2,2,0,0,0,3,2,2,3,1,3,1,0,1,2,1,0,1,3,3};
		double purity = Purity(A,B);
		System.out.println("purity		"+purity);
		System.out.println("Pre		"+Precision(A,B));
		System.out.println("Recall		"+Recall(A,B));
		System.out.println("RI(Accuracy)		"+RI(A,B));
		System.out.println("Fvalue		"+F_score(A,B));
		System.out.println("NMI		"+NMI(A,B));
		
	}
	/*
	 * 计算一个聚类结果的簇的个数，以及每一簇中的对象个数,
	 */
	public static Map<Integer,Set<Integer>> clusterDistri(int[] A){
		Map<Integer,Set<Integer>> clusterD = new HashMap<Integer,Set<Integer>>();
		int max = -1;
		for(int i = 0;i< A.length;i++){
			
			if(max < A[i]){
				max = A[i];
			}
		}
		for(int i = 0;i< A.length;i++){
			int temp = A[i];	
			if(temp < max+1){
				if(clusterD.containsKey(temp)){
					Set<Integer> set = clusterD.get(temp);
					set.add(i+1);
					clusterD.put(temp, set);
				}else{
					Set<Integer> set = new HashSet<Integer>();
					set.add(i+1);
					clusterD.put(temp, set);
				}
			}
		}
		return clusterD;
	}
	public static double ClusEvaluate(String method,int[] A,int[] B){
		
		switch(method){
		case "Purity":
			return Purity(A,B);
		case "Precision":
			return Precision(A,B);
		case "Recall":
			return Recall(A,B);
		case "RI":
			return RI(A,B);
		case "F_score":
			return F_score(A,B);
		case "NMI":
			return NMI(A,B);
		case "Jaccard":
			return Jaccard(A,B);
		default:
			return -1.0;
		}
		
	}
	public static int[] commNum(Map<Integer,Set<Integer>> A,Map<Integer,Set<Integer>> B){
		int[] commonNo = new int[A.size()];
		int com = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = A.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			Set<Integer> setA = entryA.getValue();
			Iterator<Map.Entry<Integer,Set<Integer>>> itB = B.entrySet().iterator();
			int maxComm = -1;
			while(itB.hasNext()){
				Entry<Integer,Set<Integer>> entryB = itB.next();
				Set<Integer> setB = entryB.getValue();
				int lengthA = setA.size();
				Set<Integer> temp = new HashSet<Integer>(setA);
				
				temp.removeAll(setB);
				
				int lengthCom = lengthA - temp.size();
				
				if(maxComm < lengthCom){
					maxComm = lengthCom;
				}
				
			}
			
			commonNo[i] = maxComm;
			com = com + maxComm;
			i++;
		}
		
		return commonNo;
	}
	/*
	 * 所有簇分配正确的除以总的。其中B是对比的标准标签。
	 */
	public static double Purity(int[] A,int[] B){
		double value;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);
		int[] commonNo = commNum(clusterA,clusterB);
		int com = 0;
		for(int i = 0;i<commonNo.length;i++){
			com = com + commonNo[i];
		}
		value = com*1.0/A.length;
		
		return value;
	}
	/*
	 * @param A,B
	 * @return 精度
	 */
	public static double Precision(int[] A,int[] B){
		double value = 0.0;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		int[] commonNo = commNum(clusterA,clusterB);//得到A中每个簇中聚类正确的数目。
		int allP = 0;
		int TP = 0;
		int FP = 0;
		int TN = 0;
		int FN = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			allP = allP + combination(entryA.getValue().size(),2);
			TP = TP + combination(commonNo[i],2);
			i++;
		}
		
		FP = allP - TP;
		
		itA = clusterA.entrySet().iterator();
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			
			Iterator<Map.Entry<Integer,Set<Integer>>> itA2 = clusterA.entrySet().iterator();
			while(itA2.hasNext()){
				Entry<Integer,Set<Integer>> entryA2 = itA2.next();
				if(entryA != entryA2){
					Set<Integer> s1 = entryA.getValue();
					Set<Integer> s2 = entryA2.getValue();
					for(Integer i1 :s1){
						for(Integer i2:s2){
							if(B[i1-1] != B[i2-1]){
								TN++;
							}else{
								FN++;
							}
						}
					}
					
				}
			}
		}
		
		double P = TP*1.0/(TP + FP);
		return P;
	}
	/*
	 * @param A,B
	 * @return recal召回率
	 */
	public static double Recall(int[] A,int[] B){
		double value = 0.0;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		int[] commonNo = commNum(clusterA,clusterB);//得到A中每个簇中聚类正确的数目。
		int allP = 0;
		int TP = 0;
		int FP = 0;
		int TN = 0;
		int FN = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			allP = allP + combination(entryA.getValue().size(),2);
			TP = TP + combination(commonNo[i],2);
			i++;
		}
		
		FP = allP - TP;
		
		itA = clusterA.entrySet().iterator();
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			
			Iterator<Map.Entry<Integer,Set<Integer>>> itA2 = clusterA.entrySet().iterator();
			while(itA2.hasNext()){
				Entry<Integer,Set<Integer>> entryA2 = itA2.next();
				if(entryA != entryA2){
					Set<Integer> s1 = entryA.getValue();
					Set<Integer> s2 = entryA2.getValue();
					for(Integer i1 :s1){
						for(Integer i2:s2){
							if(B[i1-1] != B[i2-1]){
								TN++;
							}else{
								FN++;
							}
						}
					}
					
				}
			}
		}
		

		double R = TP * 1.0/(TP + FN);
		return R;
	}
	/*
	 * @param A,B
	 * @return RankIndex
	 */
	public static double RI(int[] A,int[] B){
		
		double value = 0.0;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		int[] commonNo = commNum(clusterA,clusterB);//得到A中每个簇中聚类正确的数目。
		int P = 0;
		int TP = 0;
		int FP = 0;
		int TN = 0;
		int FN = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			P = P + combination(entryA.getValue().size(),2);
			TP = TP + combination(commonNo[i],2);
			i++;
		}
		
		FP = P - TP;
		
		itA = clusterA.entrySet().iterator();
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			
			Iterator<Map.Entry<Integer,Set<Integer>>> itA2 = clusterA.entrySet().iterator();
			while(itA2.hasNext()){
				Entry<Integer,Set<Integer>> entryA2 = itA2.next();
				if(entryA != entryA2){
					Set<Integer> s1 = entryA.getValue();
					Set<Integer> s2 = entryA2.getValue();
					for(Integer i1 :s1){
						for(Integer i2:s2){
							if(B[i1-1] != B[i2-1]){
								TN++;
							}else{
								FN++;
							}
						}
					}
					
				}
			}
		}
		value = (TP + TN)*1.0/(TP + FP + FN + TN);
		
		return value;
	}
	
	/*
	 * F值，是对精度和召回率的平衡，
	 * @param A:评估对象。B：评估标准；beta：均衡参数
	 * @return F值
	 */
	public static double F_score(int[] A,int[] B){

		double beta = 1.0;
		double value = 0.0;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		int[] commonNo = commNum(clusterA,clusterB);//得到A中每个簇中聚类正确的数目。
		int allP = 0;
		int TP = 0;
		int FP = 0;
		int TN = 0;
		int FN = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			allP = allP + combination(entryA.getValue().size(),2);
			TP = TP + combination(commonNo[i],2);
			i++;
		}
		
		FP = allP - TP;
		
		itA = clusterA.entrySet().iterator();
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			
			Iterator<Map.Entry<Integer,Set<Integer>>> itA2 = clusterA.entrySet().iterator();
			while(itA2.hasNext()){
				Entry<Integer,Set<Integer>> entryA2 = itA2.next();
				if(entryA != entryA2){
					Set<Integer> s1 = entryA.getValue();
					Set<Integer> s2 = entryA2.getValue();
					for(Integer i1 :s1){
						for(Integer i2:s2){
							if(B[i1-1] != B[i2-1]){
								TN++;
							}else{
								FN++;
							}
						}
					}
					
				}
			}
		}
		
		double P = TP*1.0/(TP + FP);
		double R = TP * 1.0/(TP + FN);
		value = (beta*beta + 1)*P * R/(beta*beta*P + R);
		return value;
	}
	
	public static double Jaccard(int[] A,int[] B){

		double value = 0.0;
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		int[] commonNo = commNum(clusterA,clusterB);//得到A中每个簇中聚类正确的数目。
		int allP = 0;
		int TP = 0;
		int FP = 0;
		int TN = 0;
		int FN = 0;
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		int i = 0;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			allP = allP + combination(entryA.getValue().size(),2);
			TP = TP + combination(commonNo[i],2);
			i++;
		}
		
		FP = allP - TP;
		
		itA = clusterA.entrySet().iterator();
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			
			Iterator<Map.Entry<Integer,Set<Integer>>> itA2 = clusterA.entrySet().iterator();
			while(itA2.hasNext()){
				Entry<Integer,Set<Integer>> entryA2 = itA2.next();
				if(entryA != entryA2){
					Set<Integer> s1 = entryA.getValue();
					Set<Integer> s2 = entryA2.getValue();
					for(Integer i1 :s1){
						for(Integer i2:s2){
							if(B[i1-1] != B[i2-1]){
								TN++;
							}else{
								FN++;
							}
						}
					}
					
				}
			}
		}
		
		
		value = TP * 1.0 / (TP + FP + FN);
		return value;
	}
	public static double NMI(int[] A,int[] B){
		Map<Integer,Set<Integer>> clusterA = clusterDistri(A);//得到聚类结果A的类分布
		Map<Integer,Set<Integer>> clusterB = clusterDistri(B);//得到聚类B（标准）的类分布
		Iterator<Map.Entry<Integer,Set<Integer>>> itA = clusterA.entrySet().iterator();
		
		Iterator<Map.Entry<Integer,Set<Integer>>> itB = clusterB.entrySet().iterator();
		
		Set<Set<Integer>> partitionF = new HashSet<Set<Integer>>();
		Set<Set<Integer>> partitionR = new HashSet<Set<Integer>>();
		int nodeCount = B.length;
		while(itA.hasNext()){
			Entry<Integer,Set<Integer>> entryA = itA.next();
			Set<Integer> setA = entryA.getValue();
			partitionF.add(setA);
			setA = null;
			entryA = null;
		}

		
		while(itB.hasNext()){
			Entry<Integer,Set<Integer>> entryB = itB.next();
			Set<Integer> setB = entryB.getValue();
			partitionR.add(setB);
			setB = null;
			entryB = null;
		}
		return computeNMI(partitionF,partitionR,nodeCount);
	}
	public static double computeNMI(Set<Set<Integer>> partitionF,
			Set<Set<Integer>> partitionR,int nodeCount) {
		int[][] XY = new int[partitionR.size()][partitionF.size()];
		int[] X = new int[partitionR.size()];
		int[] Y = new int[partitionF.size()];
		int i = 0;
		int j = 0;
		
		for (Set<Integer> com1 : partitionR) {
			j = 0;
			
			for (Set<Integer> com2 : partitionF) {
				
				XY[i][j] = intersect(com1, com2);//待测结果第i个簇和标准结果第j个簇的共有元素个数
				X[i] += XY[i][j];//待测结果第i个簇与所有标准结果簇的公共元素个数（感觉就是第i个簇的元素个数）
				Y[j] += XY[i][j];//标准结果簇第j个簇的元素个数（）
		
				j++;
			}
			i++;
		}
		int N = nodeCount;
		double Ixy = 0;
		double Ixy2 = 0;
		for (i = 0; i < partitionR.size(); i++) {
			for (j = 0; j < partitionF.size(); j++) {
				if (XY[i][j] > 0) {
					Ixy += ((double) XY[i][j] / N)
							* (Math.log((double) XY[i][j] * N / (X[i] * Y[j])) / Math
									.log(2.0));
//					Ixy2 = (float) (Ixy2 + -2.0D * XY[i][j]
//							* Math.log(XY[i][j] * N / X[i] * Y[j]));
				}
			}
		}
//		System.out.println(Ixy2);
//		double denom = 0.0F;
//		for (int ii = 0; ii < X.length; ++ii)
//			denom = (double) (denom + X[ii] * Math.log(X[ii] / N));
//		for (int jj = 0; jj < Y.length; ++jj) {
//			denom = (double) (denom + Y[jj] * Math.log(Y[jj] / N));
//		}
//
//		System.out.println(denom);
//		double M = (Ixy / denom);
//		
//		return M;
		
		double Hx = 0;
		double Hy = 0;
		for (i = 0; i < partitionR.size(); i++) {
			if (X[i] > 0)
				Hx += h((double) X[i] / N);
		}
		for (j = 0; j < partitionF.size(); j++) {
			if (Y[j] > 0)
				Hy += h((double) Y[j] / N);
		}
		
		double InormXY = Ixy / Math.sqrt(Hx * Hy);
		return InormXY;
	}
	private static double h(double p) {
		return -p * (Math.log(p) / Math.log(2.0));
	}
	/*
	 * 两个集合的公共元素个数
	 */
	private static int intersect(Set<Integer> com1, Set<Integer> com2) {
		int num = 0;
		for (Integer v1 : com1) {
			if (com2.contains(v1))
				num++;
		}
		return num;
	}
	/*
	 * C(m,n)=m取n
	 */
	public static int combination(int m,int n){
		int result = 1;
		if(m < n){
			return -1;
		}
		result = factorial(m)/(factorial(n)*factorial(m-n));
		
		return result;
	}
	
	public static int factorial(int m){
		
		if((m == 1) || (m == 0)){
			return 1;
		}else if(m < 0){
			return -1;
		}else{
			return m*factorial(m-1);
		}
	}
}