1.FCM模糊聚类原理

模糊c均值聚类FCM算法融合了模糊理论的精髓，相较于k-means的硬聚类，FCM算法（Fuzzy C-Means，FCM）提供了更加灵活的聚类结果。因为大部分情况下，数据集中的对象不能划分成为明显分离的簇，将一个对象划分到一个特定的簇有些生硬，不符合人的客观认知。因此，对每个对象和每个簇赋予一个权值，指明对象属于该簇的程度即可。当然，基于概率的方法也可以给出这样的权值，但是有时候我们很难确定一个合适的统计模型，因此使用具有自然地、非概率特性的FCM聚类算法就是一个比较好的选择。

2.FCM模糊聚类流程

 

3.FCM模糊聚类程序

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("iris.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U 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 fig = plt.gcf() fig.set_size_inches(16.5, 12.5) f1 = plt.figure(1) plt.scatter(datas[nonzero(label == 0), 0], datas[nonzero(label == 0), 1], marker='o', color='r', label='0', s=10) plt.scatter(datas[nonzero(label == 1), 0], datas[nonzero(label == 1), 1], marker='+', color='b', label='1', s=10) plt.scatter(datas[nonzero(label == 2), 0], datas[nonzero(label == 2), 1], marker='*', color='g', label='2', s=10) plt.scatter(center_array[:, 0], center_array[:, 1], marker='x', color='m', s=30) plt.show()