python中kmeans_kmeans与kmeans++的python实现

K-means是一种常用的聚类算法，而K-means++是K-means算法的优化版本，它能够更好地初始化聚类中心，从而得到更好的聚类效果。下面是Python中K-means和K-means++的实现方法。

K-means实现：

import numpy as np

def kmeans(X, k, max_iter=100):
    n_samples, n_features = X.shape
    centroids = X[np.random.choice(n_samples, k, replace=False)]
    for i in range(max_iter):
        clusters = [[] for _ in range(k)]
        for idx, x in enumerate(X):
            distances = [np.linalg.norm(x - c) for c in centroids]
            clusters[np.argmin(distances)].append(idx)
        new_centroids = np.zeros((k, n_features))
        for idx, cluster in enumerate(clusters):
            new_centroids[idx] = np.mean(X[cluster], axis=0)
        if np.allclose(new_centroids, centroids):
            break
        centroids = new_centroids
    return centroids, clusters

K-means++实现：

import numpy as np

def kmeans_pp(X, k, max_iter=100):
    n_samples, n_features = X.shape
    centroids = []
    # choose first centroid randomly
    idx = np.random.choice(n_samples, 1, replace=False)
    centroids.append(X[idx])
    # choose the rest of the centroids using k-means++ algorithm
    for i in range(1, k):
        distances = np.zeros(n_samples)
        for j, x in enumerate(X):
            distances[j] = np.min([np.linalg.norm(x - c) for c in centroids])
        probabilities = distances / np.sum(distances)
        cumulative_probabilities = np.cumsum(probabilities)
        idx = np.searchsorted(cumulative_probabilities, np.random.rand())
        centroids.append(X[idx])
    centroids = np.array(centroids)
    # run k-means algorithm with the initial centroids
    for i in range(max_iter):
        clusters = [[] for _ in range(k)]
        for idx, x in enumerate(X):
            distances = [np.linalg.norm(x - c) for c in centroids]
            clusters[np.argmin(distances)].append(idx)
        new_centroids = np.zeros((k, n_features))
        for idx, cluster in enumerate(clusters):
            new_centroids[idx] = np.mean(X[cluster], axis=0)
        if np.allclose(new_centroids, centroids):
            break
        centroids = new_centroids
    return centroids, clusters

这两个函数的输入参数相同，其中X是数据集，k是聚类数量，max_iter是最大迭代次数。函数返回聚类中心和每个数据点所属的聚类编号。