Python实现K-Means聚类实例

以下是Python实现K-Means聚类的代码示例：

import numpy as np
from matplotlib import pyplot as plt

# 生成数据点
X = np.array([[1, 2], [1.5, 1.8], [5, 8], [8, 8], [1, 0.6], [9, 11]])
# 设定初始聚类中心
centroids = np.array([[1, 0.6], [1.5, 1.8], [5, 8]])

# 定义距离函数
def euclidean_distance(x1, x2):
    return np.sqrt(np.sum((x1 - x2) ** 2))

# 定义K-Means函数
def k_means(X, k=3, max_iters=100):
    # 随机初始化聚类中心
    idx = np.random.choice(len(X), k, replace=False)
    centroids = X[idx]
    
    # 迭代更新聚类中心
    for i in range(max_iters):
        # 分配数据点到最近的聚类中心
        clusters = [[] for _ in range(k)]
        for x in X:
            distances = [euclidean_distance(x, c) for c in centroids]
            cluster_idx = np.argmin(distances)
            clusters[cluster_idx].append(x)
        
        # 计算新的聚类中心
        new_centroids = []
        for c in clusters:
            mean = np.mean(c, axis=0)
            new_centroids.append(mean)
        new_centroids = np.array(new_centroids)
        
        # 判断是否收敛
        if np.all(centroids == new_centroids):
            break
        
        centroids = new_centroids
    
    return centroids, clusters

# 调用K-Means函数
centroids, clusters = k_means(X, k=3)

# 可视化聚类结果
colors = ['r', 'g', 'b']
for i, c in enumerate(clusters):
    for x in c:
        plt.scatter(x[0], x[1], color=colors[i])
plt.scatter(centroids[:,0], centroids[:,1], marker='*', s=200, color='black')
plt.show()

运行上述代码，可以得到类似于以下图像的聚类结果：