fcm聚类 python

FCM（模糊C均值）聚类算法是一种常用的模糊聚类算法，用来对数据进行聚类。它的基本思路是通过初始化一个隶属度矩阵U，然后根据U计算类中心矩阵C，再根据C重新计算U。这两个步骤循环迭代直到满足循环条件，最后得到聚类结果。

以下是FCM聚类算法的Python实现的核心代码：

import numpy as np

def fcm(data, c, m, epsilon, max_iter):
    n = data.shape[0]
    d = data.shape[1]
    U = np.random.rand(n, c)
    U = U / np.sum(U, axis=1)[:, np.newaxis]
    C = np.zeros((c, d))
    for i in range(max_iter):
        prev_U = U.copy()
        for j in range(c):
            numerator = np.sum((U[:, j] ** m)[:, np.newaxis] * data, axis=0)
            denominator = np.sum(U[:, j] ** m)
            C[j] = numerator / denominator
        dist = np.linalg.norm(data[:, np.newaxis, :] - C, axis=2)
        U = 1 / (np.power(dist,2 / (m - 1)).reshape((n, c)) + epsilon)
        U = U / np.sum(U, axis=1)[:, np.newaxis]
        if np.linalg.norm(U - prev_U) < epsilon:
            break
    return U, C

# 使用示例
data = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
c = 2
m = 2
epsilon = 1e-3
max_iter = 100
U, C = fcm(data, c, m, epsilon, max_iter)