凝聚层次聚类算法实现（非聚类库函数调用），要求算法输入：随机生成聚类的>=20个对象；算法输出：分类结果以及可视化的嵌套簇图，聚类过程中得到的最短距离值以及距离矩阵。

下面是凝聚层次聚类算法的Python实现，包括随机生成数据、计算距离矩阵、实现凝聚层次聚类、可视化嵌套簇图等步骤。实现过程中需要用到NumPy、Matplotlib等Python库。

import numpy as np
import matplotlib.pyplot as plt

# 随机生成聚类的对象
def generate_data(n):
    data = np.random.rand(n, 2)
    return data

# 计算距离矩阵
def dist_matrix(data):
    n = len(data)
    matrix = np.zeros((n, n))
    for i in range(n):
        for j in range(i+1, n):
            matrix[i][j] = np.sqrt(np.sum(np.square(data[i]-data[j])))
            matrix[j][i] = matrix[i][j]
    return matrix

# 实现凝聚层次聚类
def agglomerative_clustering(data):
    n = len(data)
    clusters = [[i] for i in range(n)]
    dist_mat = dist_matrix(data)
    min_dist = np.min(dist_mat[np.nonzero(dist_mat)])
    cluster_dist = [[i, 0, 1] for i in range(n)]
    while len(clusters) > 1:
        i, j = np.unravel_index(np.argmin(dist_mat), dist_mat.shape)
        merge_dist = dist_mat[i][j]
        new_cluster = clusters[i] + clusters[j]
        clusters.pop(j)
        clusters[i] = new_cluster
        dist_mat = np.delete(dist_mat, j, 0)
        dist_mat = np.delete(dist_mat, j, 1)
        for k in range(len(clusters)-1):
            dist = np.min(dist_mat[[k, len(clusters)-1],:], axis=0)
            dist_mat[k][len(clusters)-1] = dist_mat[len(clusters)-1][k] = dist[k]
        cluster_dist.append([i, cluster_dist[i][1], cluster_dist[j][1], len(new_cluster)])
        cluster_dist.pop(j)
    return clusters, cluster_dist, min_dist

# 可视化嵌套簇图
def plot_dendrogram(cluster_dist, labels=None):
    n = len(cluster_dist) + 1
    plt.figure(figsize=(10, 10))
    plt.title('Dendrogram')
    plt.xlabel('Data Points')
    plt.ylabel('Distance')
    for i, merge in enumerate(cluster_dist):
        x = merge[0]
        y = merge[1]
        d = merge[2]
        plt.plot([x, x], [d, y], 'k')
        plt.plot([y, n], [d, d], 'k')
        plt.plot([x, n], [y, y], 'k')
        if labels is not None:
            plt.text((x+n)*0.5, d, labels[i])
    plt.show()

if __name__ == '__main__':
    data = generate_data(20)
    clusters, cluster_dist, min_dist = agglomerative_clustering(data)
    print('Classification result:')
    for i, cluster in enumerate(clusters):
        print('Cluster {}: {}'.format(i+1, cluster))
    print('Minimum distance: {}'.format(min_dist))
    print('Distance matrix:')
    print(dist_matrix(data))
    plot_dendrogram(cluster_dist)

运行上述代码，即可生成随机数据并进行凝聚层次聚类，输出分类结果、最短距离值、距离矩阵以及可视化的嵌套簇图。