最短距离的层次聚类算法python实现

以下是一个基于Python的层次聚类算法的实现：

import numpy as np

def euclidean_distance(x, y):
    """
    计算欧几里得距离
    """
    return np.sqrt(np.sum((x - y) ** 2))

def hierarchical_clustering(data, method='single'):
    """
    层次聚类算法实现
    :param data: 二维数据集，每行代表一个样本
    :param method: 距离计算方法，包括'single', 'complete', 'average'和'centroid'
    :return: 聚类结果，每个元素代表一个聚类，元素为聚类中心的下标
    """
    n = data.shape[0]
    # 初始化距离矩阵
    distances = np.zeros((n, n))
    for i in range(n):
        for j in range(i+1, n):
            distances[i, j] = euclidean_distance(data[i], data[j])
            distances[j, i] = distances[i, j]

    # 初始化聚类标号
    clusters = np.arange(n)

    # 合并聚类
    for k in range(n-1):
        # 找到距离最小的两个聚类
        i, j = np.unravel_index(np.argmin(distances), distances.shape)
        # 合并聚类
        clusters[clusters == clusters[j]] = clusters[i]
        # 更新距离矩阵
        if method == 'single':
            distances[i, :] = np.minimum(distances[i, :], distances[j, :])
            distances[:, i] = distances[i, :]
        elif method == 'complete':
            distances[i, :] = np.maximum(distances[i, :], distances[j, :])
            distances[:, i] = distances[i, :]
        elif method == 'average':
            distances[i, :] = (distances[i, :] + distances[j, :]) / 2
            distances[:, i] = distances[i, :]
        elif method == 'centroid':
            centroid = (data[clusters == i].mean(axis=0) + data[clusters == j].mean(axis=0)) / 2
            distances[i, :] = euclidean_distance(centroid, data)
            distances[:, i] = distances[i, :]
        else:
            raise ValueError("Invalid method")
        distances[i, i] = np.inf
        distances[j, :] = np.inf
        distances[:, j] = np.inf

    # 返回聚类结果
    return np.unique(clusters)

可以通过调用函数 `hierarchical_clustering(data, method)` 来实现层次聚类。其中，`data` 是一个二维的数据集，每行代表一个样本；`method` 是距离计算方法，包括'single', 'complete', 'average'和'centroid'。函数返回聚类结果，每个元素代表一个聚类，元素为聚类中心的下标。