PAM算法python实例

PAM（Partitioning Around Medoids）算法是一种基于贪心策略的聚类算法，它的思想是选择一部分数据作为簇的代表点（medoids），然后将其它数据点分配到最近的代表点所在的簇中。PAM算法相对于K-Means算法的优点在于它可以处理离群点（outliers）。

下面是一个使用Python实现PAM算法的示例代码：

import numpy as np

def distance(point1, point2):
    """计算两个点之间的欧几里德距离"""
    return np.sqrt(np.sum((point1 - point2) ** 2))

def pam(dataset, k):
    """PAM算法"""
    # 随机选择k个点作为medoids
    medoids = dataset[np.random.choice(len(dataset), k, replace=False)]
    # 初始化簇
    clusters = [[] for _ in range(k)]
    # 将每个点分配到最近的medoid所在的簇中
    for point in dataset:
        distances = [distance(point, medoid) for medoid in medoids]
        nearest_medoid = np.argmin(distances)
        clusters[nearest_medoid].append(point)
    # 计算当前聚类的SSE（误差平方和）
    sse = sum([sum([distance(point, medoids[i]) ** 2 for point in cluster]) for i, cluster in enumerate(clusters)])
    # 进行迭代，直到SSE不再变化
    while True:
        # 对于每个medoid，尝试用其它簇中的点替换它，并计算SSE的变化
        for i in range(k):
            for j in range(len(clusters[i])):
                if not np.array_equal(clusters[i][j], medoids[i]):
                    new_medoid = clusters[i][j]
                    new_clusters = clusters.copy()
                    new_clusters[i].remove(clusters[i][j])
                    distances = [distance(point, new_medoid) for point in new_clusters[i]]
                    nearest_medoid = np.argmin(distances)
                    new_clusters[nearest_medoid].append(medoids[i])
                    new_sse = sum([sum([distance(point, new_medoids[i]) ** 2 for point in new_cluster]) for i, new_cluster in enumerate(new_clusters)])
                    if new_sse < sse:
                        medoids[i] = new_medoid
                        clusters = new_clusters
                        sse = new_sse
                        break
            else:
                continue
            break
        else:
            break
    return clusters

使用示例：

import matplotlib.pyplot as plt

# 生成随机数据
np.random.seed(0)
dataset = np.random.randn(100, 2)

# 聚类
clusters = pam(dataset, 3)

# 绘制结果
colors = ['r', 'g', 'b']
for i, cluster in enumerate(clusters):
    for point in cluster:
        plt.scatter(point[0], point[1], color=colors[i])
plt.show()

输出结果：