粒kmeans聚类算法的代码

以下是粒kmeans聚类算法的Python代码：

import numpy as np
from scipy.spatial.distance import cdist

def generate_fuzzy_membership(data, centers, m):
    """
    生成模糊成员关系
    :param data: 样本数据, shape为(n_samples, n_features)
    :param centers: 聚类中心, shape为(n_clusters, n_features)
    :param m: 模糊指数
    :return: 模糊成员关系, shape为(n_samples, n_clusters)
    """
    # 计算样本到聚类中心的距离
    distance = cdist(data, centers)
    # 初始化模糊成员关系矩阵
    membership = np.zeros((data.shape[0], centers.shape[0]))
    for i in range(data.shape[0]):
        for j in range(centers.shape[0]):
            # 根据公式计算模糊成员关系
            u = np.power(distance[i, j]/distance[i], 2/(m-1))
            membership[i, j] = 1/np.sum(u)
    return membership

def generate_centers(data, membership, m):
    """
    生成新的聚类中心
    :param data: 样本数据, shape为(n_samples, n_features)
    :param membership: 模糊成员关系, shape为(n_samples, n_clusters)
    :param m: 模糊指数
    :return: 新的聚类中心, shape为(n_clusters, n_features)
    """
    # 初始化聚类中心矩阵
    centers = np.zeros((membership.shape[1], data.shape[1]))
    for j in range(membership.shape[1]):
        # 根据公式计算新的聚类中心
        centers[j, :] = np.sum(np.power(membership[:, j], m).reshape((-1, 1))*data, axis=0)/np.sum(np.power(membership[:, j], m))
    return centers

def calculate_obj_func(data, centers, membership, m):
    """
    计算目标函数
    :param data: 样本数据, shape为(n_samples, n_features)
    :param centers: 聚类中心, shape为(n_clusters, n_features)
    :param membership: 模糊成员关系, shape为(n_samples, n_clusters)
    :param m: 模糊指数
    :return: 目标函数
    """
    # 计算样本到聚类中心的距离
    distance = cdist(data, centers)
    return np.sum(membership**m*distance**2)

def fuzzy_kmeans(data, n_clusters, m=2, max_iter=100, tol=1e-4):
    """
    粒kmeans聚类算法
    :param data: 样本数据, shape为(n_samples, n_features)
    :param n_clusters: 聚类数量
    :param m: 模糊指数, 默认值为2
    :param max_iter: 最大迭代次数, 默认值为100
    :param tol: 容差, 默认值为0.0001
    :return: 聚类标签和聚类中心
    """
    # 初始化聚类中心
    centers = data[np.random.choice(data.shape[0], size=n_clusters, replace=False), :]
    # 初始化模糊成员关系
    membership = generate_fuzzy_membership(data, centers, m)
    # 初始化迭代次数
    n_iter = 0
    # 初始化目标函数
    obj_func = calculate_obj_func(data, centers, membership, m)
    # 开始迭代
    while n_iter < max_iter:
        # 生成新的聚类中心
        new_centers = generate_centers(data, membership, m)
        # 计算新的模糊成员关系
        new_membership = generate_fuzzy_membership(data, new_centers, m)
        # 计算新的目标函数
        new_obj_func = calculate_obj_func(data, new_centers, new_membership, m)
        # 如果目标函数变化小于容差，则算法收敛，退出迭代
        if np.abs(new_obj_func - obj_func) < tol:
            break
        else:
            # 否则更新聚类中心和模糊成员关系，并增加迭代次数
            centers = new_centers
            membership = new_membership
            obj_func = new_obj_func
            n_iter += 1
    # 返回聚类标签和聚类中心
    labels = np.argmax(membership, axis=1)
    return labels, centers

使用示例：

from sklearn.datasets import make_blobs

# 生成样本数据
data, labels = make_blobs(n_samples=1000, centers=3, random_state=10)

# 使用粒kmeans算法进行聚类
n_clusters = 3
labels_pred, centers = fuzzy_kmeans(data, n_clusters, m=2, max_iter=100, tol=1e-4)

# 可视化聚类结果
import matplotlib.pyplot as plt
plt.scatter(data[:, 0], data[:, 1], c=labels_pred)
plt.scatter(centers[:, 0], centers[:, 1], marker='x', color='red', linewidths=2)
plt.show()