层次聚类Single Link (MIN) python代码

下面是一个基于Python的单链接（Single Link）层次聚类算法的示例代码：

import numpy as np

def single_linkage(X, k):
    """
    Single Linkage Clustering
    X: ndarray, shape(n_samples, n_features)
    k: int, the number of clusters
    """
    n_samples = X.shape[0]
    # initialize the distance matrix
    dist_matrix = np.zeros((n_samples, n_samples))
    for i in range(n_samples):
        for j in range(i+1, n_samples):
            dist_matrix[i, j] = np.linalg.norm(X[i] - X[j])
            dist_matrix[j, i] = dist_matrix[i, j]

    # initialize the clusters
    clusters = [[i] for i in range(n_samples)]

    # merge clusters iteratively
    while len(clusters) > k:
        # find the closest pair of clusters
        min_dist = np.inf
        for i in range(len(clusters)):
            for j in range(i+1, len(clusters)):
                dist = np.min(dist_matrix[np.ix_(clusters[i], clusters[j])])
                if dist < min_dist:
                    min_dist = dist
                    merge_pair = (i, j)

        # merge the two closest clusters
        new_cluster = clusters[merge_pair[0]] + clusters[merge_pair[1]]
        clusters.pop(merge_pair[1])
        clusters[merge_pair[0]] = new_cluster

        # update the distance matrix
        for i in range(len(clusters)-1):
            dist_matrix[i, merge_pair[0]] = np.min(dist_matrix[np.ix_(clusters[i], new_cluster)])
            dist_matrix[merge_pair[0], i] = dist_matrix[i, merge_pair[0]]

        dist_matrix[merge_pair[0], merge_pair[0]] = np.inf

    return clusters

其中，输入参数`X`是数据集，`k`是期望的聚类数。`dist_matrix`是距离矩阵，用来记录每个样本之间的距离。`clusters`是一个列表，每个元素是一个聚类簇的索引列表。在每次迭代中，找到距离最近的一对聚类簇，将它们合并成一个新的聚类簇，并更新距离矩阵。最终返回聚类结果。