NMI计算

NMI计算

NMI(Normalized Mutual Information)标准化互信息，常用在聚类中，度量两个聚类结果的相近程度。是社区发现(community detection)的重要衡量指标，基本可以比较客观地评价出一个社区划分与标准划分之间相比的准确度。NMI的值域是0到1，越高代表划分得越准。

# -*- coding:utf-8 -*-
'''
Created on 2017年10月28日

@summary: 利用Python实现NMI计算

@author: dreamhome
'''
import math
import numpy as np
from sklearn import metrics
def NMI(A,B):
    #样本点数
    total = len(A)
    A_ids = set(A)
    B_ids = set(B)
    #互信息计算
    MI = 0
    eps = 1.4e-45
    for idA in A_ids:
        for idB in B_ids:
            idAOccur = np.where(A==idA)
            idBOccur = np.where(B==idB)
            idABOccur = np.intersect1d(idAOccur,idBOccur)
            px = 1.0*len(idAOccur[0])/total
            py = 1.0*len(idBOccur[0])/total
            pxy = 1.0*len(idABOccur)/total
            MI = MI + pxy*math.log(pxy/(px*py)+eps,2)
    # 标准化互信息
    Hx = 0
    for idA in A_ids:
        idAOccurCount = 1.0*len(np.where(A==idA)[0])
        Hx = Hx - (idAOccurCount/total)*math.log(idAOccurCount/total+eps,2)
    Hy = 0
    for idB in B_ids:
        idBOccurCount = 1.0*len(np.where(B==idB)[0])
        Hy = Hy - (idBOccurCount/total)*math.log(idBOccurCount/total+eps,2)
    MIhat = 2.0*MI/(Hx+Hy)
    return MIhat

if __name__ == '__main__':
    A = np.array([1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3])
    B = np.array([1,2,1,1,1,1,1,2,2,2,2,3,1,1,3,3,3])
    print NMI(A,B)
    print metrics.normalized_mutual_info_score(A,B)


原文：https://blog.csdn.net/DreamHome_S/article/details/78379635 

# coding=utf-8
import numpy as np
import math
def NMI(A,B):
    # len(A) should be equal to len(B)
    total = len(A)
    A_ids = set(A)
    B_ids = set(B)
    #Mutual information
    MI = 0
    eps = 1.4e-45
    for idA in A_ids:
        for idB in B_ids:
            idAOccur = np.where(A==idA)
            idBOccur = np.where(B==idB)
            idABOccur = np.intersect1d(idAOccur,idBOccur)
            px = 1.0*len(idAOccur[0])/total
            py = 1.0*len(idBOccur[0])/total
            pxy = 1.0*len(idABOccur)/total
            MI = MI + pxy*math.log(pxy/(px*py)+eps,2)
    # Normalized Mutual information
    Hx = 0
    for idA in A_ids:
        idAOccurCount = 1.0*len(np.where(A==idA)[0])
        Hx = Hx - (idAOccurCount/total)*math.log(idAOccurCount/total+eps,2)
    Hy = 0
    for idB in B_ids:
        idBOccurCount = 1.0*len(np.where(B==idB)[0])
        Hy = Hy - (idBOccurCount/total)*math.log(idBOccurCount/total+eps,2)
    MIhat = 2.0*MI/(Hx+Hy)
    return MIhat

if __name__ == '__main__':
    A = np.array([1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3])
    B = np.array([1,2,1,1,1,1,1,2,2,2,2,3,1,1,3,3,3])
    print (NMI(A,B))

结果：0.36456

这一篇博文写的不错

自己编写了一个，同时做了排序处理

# coding=utf-8
import numpy as np
import math
import operator


def NMI(A,B):
    # len(A) should be equal to len(B)
    total = len(A)
    A_ids = set(A)
    B_ids = set(B)
    #Mutual information
    MI = 0
    eps = 1.4e-45
    for idA in A_ids:
        for idB in B_ids:
            idAOccur = np.where(A==idA)
            idBOccur = np.where(B==idB)
            idABOccur = np.intersect1d(idAOccur,idBOccur)
            px = 1.0*len(idAOccur[0])/total
            py = 1.0*len(idBOccur[0])/total
            pxy = 1.0*len(idABOccur)/total
            MI = MI + pxy*math.log(pxy/(px*py)+eps,2)
    # Normalized Mutual information
    Hx = 0
    for idA in A_ids:
        idAOccurCount = 1.0*len(np.where(A==idA)[0])
        Hx = Hx - (idAOccurCount/total)*math.log(idAOccurCount/total+eps,2)
    Hy = 0
    for idB in B_ids:
        idBOccurCount = 1.0*len(np.where(B==idB)[0])
        Hy = Hy - (idBOccurCount/total)*math.log(idBOccurCount/total+eps,2)
    MIhat = 2.0*MI/(Hx+Hy)
    return MIhat


if __name__ == '__main__':
    A = np.array([1,1,1])
    B = np.array([2,3,4])
    C = np.array([1,1,6])
    print(NMI(A,B))
    m=[]#包含了位置的互信息
    n=[]#只有互信息
    dic={}
    q=1
    m.append(NMI(A,B))
    m.append(NMI(B,C))
    m.append(NMI(A,C))
    
    
    for i in m:
        dic['第{}个互信息'.format(q)]='{}'.format(i)
        q=q+1
    print(dic)
    rankdata=sorted(dic.items(),key=operator.itemgetter(1),reverse=True)
    print(rankdata)
    
    

实验结果如图