python实现kmeans聚类算法

import numpy as np import matplotlib.pyplot as plt def initialize_centroids(X, k): """ 随机初始化k个质心 """ m, n = X.shape centroids = X[np.random.choice(m, k, replace=False)] return centroids def closest_centroid(X, centroids): """ 计算每个点到每个质心的距离，并返回最近的质心的索引 """ m = X.shape[0] k = centroids.shape[0] distances = np.sqrt(((X - centroids[:, np.newaxis])**2).sum(axis=2)) return np.argmin(distances, axis=0) def move_centroids(X, closest, centroids): """ 根据最近的点的均值更新质心位置 """ m, n = X.shape k = centroids.shape[0] new_centroids = np.zeros((k, n)) for i in range(k): points_in_cluster = X[closest == i] new_centroids[i] = points_in_cluster.mean(axis=0) return new_centroids def kmeans(X, k, max_iters=100): """ 实现K-Means算法 """ centroids = initialize_centroids(X, k) for _ in range(max_iters): closest = closest_centroid(X, centroids) centroids = move_centroids(X, closest, centroids) return centroids, closest # 生成随机数据集 np.random.seed(0) X = np.random.randn(300, 2) # 执行K-Means聚类 k = 3 centroids, closest = kmeans(X, k) # 可视化结果 colors = ['r', 'g', 'b'] for i in range(k): points = X[closest == i] plt.scatter(points[:, 0], points[:, 1], s=50, c=colors[i], label=f'Cluster {i+1}') plt.scatter(centroids[:, 0], centroids[:, 1], s=200, c='yellow', label='Centroids') plt.legend() plt.show()