实现三支K-means算法

以下是三支K-means算法的Python代码实现：

1. 基本K-means算法

import numpy as np

def kmeans(X, k, max_iter=100):
    # 初始化质心
    centers = X[np.random.choice(X.shape[0], k, replace=False)]
    for i in range(max_iter):
        # 分配样本到最近的质心
        distances = np.sqrt(((X - centers[:, np.newaxis])**2).sum(axis=2))
        clusters = np.argmin(distances, axis=0)
        # 更新质心
        for j in range(k):
            centers[j] = X[clusters == j].mean(axis=0)
    return centers, clusters

2. K-means++算法

import numpy as np

def kmeans_pp(X, k, max_iter=100):
    # 初始化第一个质心
    centers = [X[np.random.choice(X.shape[0])]]
    for i in range(1, k):
        # 计算每个样本到最近质心的距离的平方
        distances = np.sqrt(((X - np.array(centers)[:, np.newaxis])**2).sum(axis=2)).min(axis=0)**2
        # 根据每个样本距离质心的距离的平方来选择下一个质心
        probs = distances / distances.sum()
        idx = np.random.choice(X.shape[0], p=probs)
        centers.append(X[idx])
    centers = np.array(centers)
    # 运行基本K-means算法
    for i in range(max_iter):
        distances = np.sqrt(((X - centers[:, np.newaxis])**2).sum(axis=2))
        clusters = np.argmin(distances, axis=0)
        for j in range(k):
            centers[j] = X[clusters == j].mean(axis=0)
    return centers, clusters

3. Mini-batch K-means算法

import numpy as np

def minibatch_kmeans(X, k, batch_size=100, max_iter=100):
    # 初始化质心
    centers = X[np.random.choice(X.shape[0], k, replace=False)]
    for i in range(max_iter):
        # 随机选择一个mini-batch
        batch = X[np.random.choice(X.shape[0], batch_size, replace=False)]
        # 分配样本到最近的质心
        distances = np.sqrt(((batch - centers[:, np.newaxis])**2).sum(axis=2))
        clusters = np.argmin(distances, axis=0)
        # 更新质心
        for j in range(k):
            centers[j] = np.mean(batch[clusters == j], axis=0)
    # 分配剩余样本到最近的质心
    distances = np.sqrt(((X - centers[:, np.newaxis])**2).sum(axis=2))
    clusters = np.argmin(distances, axis=0)
    return centers, clusters