模糊聚类作业-鸢尾花分类

import numpy as np

from sklearn import datasets


def FCM(X, c_clusters=3, m=2, eps=1e-2):
    # 随机二维数组shape(150,3)，初始化隶属度矩阵
    membership_mat = np.random.random((len(X), c_clusters))
    # 使Xi的隶属度总和为1，即Xi隶属于每个类别的数值求和为1
    membership_mat = np.divide(membership_mat, np.sum(membership_mat, axis=1)[:, np.newaxis])

    while True:
        # 超参数m=2
        working_membership_mat = membership_mat ** m
        # 根据公式计算聚类中心点Centroids.shape->(3,4)  C_j
        Centroids = np.divide(np.dot(working_membership_mat.T, X),
                              np.sum(working_membership_mat.T, axis=1)[:, np.newaxis])

        # 该矩阵保存所有实点到每个聚类中心的欧式距离
        n_c_distance_mat = np.zeros((len(X), c_clusters))  # shape->(150,3)

        for i, x in enumerate(X):
            for j, c in enumerate(Centroids):
                n_c_distance_mat[i][j] = np.linalg.norm(x - c, 2)  # 计算l2范数(欧氏距离)

        new_membership_mat = np.zeros((len(X), c_clusters))

        # 更新模糊矩阵U
        for i, x in enumerate(X):
            for j, c in enumerate(Centroids):
                new_membership_mat[i][j] = 1. / np.sum((n_c_distance_mat[i][j] / n_c_distance_mat[i]) ** (2 / (m - 1)))

        # 聚类到隶属度变化
        if np.sum(abs(new_membership_mat - membership_mat)) < eps:
            break

        membership_mat = new_membership_mat

    return np.argmax(new_membership_mat, axis=1)


if __name__ == '__main__':
    iris = datasets.load_iris()
    print(FCM(iris.data))