模糊K均值算法python代码实现（FCM）

# -*- coding:utf-8 -*-
from pylab import *
from numpy import*
import pandas as pd
import numpy as np
import operator
import math
import matplotlib.pyplot as plt
import random
#数据保存在.csv文件中
df_full = pd.read_csv("result.csv")
columns = list(df_full.columns)
features = columns[:len(columns)-1]
#class_labels = list(df_full[columns[-1]])
df = df_full[features]
# 维度
num_attr = len(df.columns) - 1
# 分类数
k =3
# 最大迭代数
MAX_ITER = 100
# 样本数
n = len(df)    #the number of row
# 模糊参数
m = 2.00

#初始化模糊矩阵
def initializeMembershipMatrix():
    membership_mat = list()
    for i in range(n):
        random_num_list = [random.random() for i in range(k)]
        summation = sum(random_num_list)
        temp_list = [x/summation for x in random_num_list]#首先归一化
        membership_mat.append(temp_list)
    return membership_mat

#计算类中心点
def calculateClusterCenter(membership_mat):
    cluster_mem_val = zip(*membership_mat)
    cluster_centers = list()
    cluster_mem_val_list = list(cluster_mem_val)
    for j in range(k):
        x=cluster_mem_val_list[j]
        xraised = [e ** m for e in x]
        denominator = sum(xraised)
        temp_num = list()
        for i in range(n):
            data_point = list(df.iloc[i])
            prod = [xraised[i] * val for val in data_point]
            temp_num.append(prod)
        numerator = map(sum, zip(*temp_num))
        center = [z/denominator for z in numerator]#每一维都要计算。
        cluster_centers.append(center)
    return cluster_centers

#更新隶属度
def updateMembershipValue(membership_mat, cluster_centers):
#    p = float(2/(m-1))
    data=[]
    for i in range(n):
        x = list(df.iloc[i])#取出文件中的每一行数据
        data.append(x)
        distances = [np.linalg.norm(list(map(operator.sub, x, cluster_centers[j]))) for j in range(k)]
        for j in range(k):
            den = sum([math.pow(float(distances[j]/distances[c]), 2) for c in range(k)])
            membership_mat[i][j] = float(1/den)       
    return membership_mat,data

#得到聚类结果
def getClusters(membership_mat):
    cluster_labels = list()
    for i in range(n):
        max_val, idx = max((val, idx) for (idx, val) in enumerate(membership_mat[i]))
        cluster_labels.append(idx)
    return cluster_labels

def fuzzyCMeansClustering():
    # 主程序
    membership_mat = initializeMembershipMatrix()
    curr = 0
    while curr <= MAX_ITER:#最大迭代次数
        cluster_centers = calculateClusterCenter(membership_mat)
        membership_mat,data = updateMembershipValue(membership_mat, cluster_centers)
        cluster_labels = getClusters(membership_mat)
        curr += 1
    print(membership_mat)
    return cluster_labels, cluster_centers,data,membership_mat

def xie_beni(membership_mat,center,data):
    sum_cluster_distance=0
    min_cluster_center_distance=inf
    for i in range(k):
        for j in range(n):
            sum_cluster_distance=sum_cluster_distance + membership_mat[j][i]** 2 * sum(power(data[j,:]- center[i,:],2))#计算类一致性
    for i in range(k-1):
        for j in range(i+1,k):
            cluster_center_distance=sum(power(center[i,:]-center[j,:],2))#计算类间距离
            if cluster_center_distance<min_cluster_center_distance:
                min_cluster_center_distance=cluster_center_distance
    return sum_cluster_distance/(n*min_cluster_center_distance)
labels,centers,data,membership= fuzzyCMeansClustering()
print(labels)
print(centers)
center_array=array(centers)
label=array(labels)
datas=array(data)

#Xie-Beni聚类有效性
print("聚类有效性：",xie_beni(membership,center_array,datas))
xlim(0, 10)
ylim(0, 10)
#做散点图
f1 = plt.figure(1)
plt.scatter(datas[nonzero(label==0),0],datas[nonzero(label==0),1],marker='o',color='r',label='0',s=30)
plt.scatter(datas[nonzero(label==1),0],datas[nonzero(label==1),1],marker='+',color='b',label='1',s=30)
plt.scatter(datas[nonzero(label==2),0],datas[nonzero(label==2),1],marker='*',color='g',label='2',s=30)
plt.scatter(center_array[:,0],center_array[:,1],marker = 'x', color = 'm', s = 50)
plt.show()

程序运行结果：