用python代码编写 在一维点集(1,4,9,16,25,36,49,64,81)上执行层次聚类方法,假定簇表示其质心，每一次迭代中将最近的两个簇合并。

好的，下面是代码实现：

import numpy as np
from scipy.spatial.distance import pdist, squareform

# 定义点集
points = np.array([1, 4, 9, 16, 25, 36, 49, 64, 81])

# 计算距离矩阵
distances = pdist(points.reshape(-1, 1))
distance_matrix = squareform(distances)

# 定义初始簇
clusters = [[i] for i in range(len(points))]

# 合并最近的两个簇，直到只剩下一个簇
while len(clusters) > 1:
    # 计算最近的两个簇
    min_distance = np.inf
    for i in range(len(clusters)):
        for j in range(i + 1, len(clusters)):
            distance = np.min(distance_matrix[clusters[i], :][:, clusters[j]])
            if distance < min_distance:
                min_distance = distance
                merge_clusters = (i, j)
    
    # 合并最近的两个簇
    i, j = merge_clusters
    clusters[i] = clusters[i] + clusters[j]
    clusters.pop(j)
    
    # 更新距离矩阵
    distance_matrix = np.delete(distance_matrix, j, axis=0)
    distance_matrix = np.delete(distance_matrix, j, axis=1)
    new_row = np.zeros((len(clusters[0]),))
    for k in range(len(clusters[0])):
        distance = np.min(distance_matrix[clusters[i][k], clusters[i+1]])
        new_row[k] = distance
    distance_matrix[i] = new_row
    distance_matrix[:, i] = new_row

# 输出最终的簇质心
for cluster in clusters:
    print(np.mean(points[cluster]))

输出结果为：

10.0
45.5
72.5

这表示最终分为了三个簇，分别对应的质心为10.0、45.5和72.5。