分裂聚类对鸢尾花数据集聚类

对于分裂聚类（Divisive clustering），我们需要先定义一个初始聚类，然后递归地将每个聚类分裂成更小的聚类，直到满足某个终止条件为止。这里我们可以使用 K-means 算法作为初始聚类，然后通过距离度量来分裂聚类。

首先，我们导入必要的库：

from sklearn.datasets import load_iris
from sklearn.cluster import KMeans
from scipy.spatial.distance import cdist
import numpy as np

然后，我们加载鸢尾花数据集并获取特征：

iris = load_iris()
X = iris.data

接下来，我们使用 K-means 算法作为初始聚类：

kmeans = KMeans(n_clusters=3).fit(X)

然后，我们定义一个分裂函数，用于将聚类分裂成更小的聚类。这里我们使用了欧几里得距离度量：

def split_cluster(cluster, X):
    # Compute the distance matrix between points and the centroid of the cluster
    distances = cdist(X, np.mean(cluster, axis=0).reshape(1, -1))
    
    # Identify the point farthest from the centroid
    farthest_idx = np.argmax(distances)
    
    # Split the cluster into two sub-clusters
    sub_clusters = np.split(cluster, [farthest_idx], axis=0)
    
    # Compute the centroids of the sub-clusters
    centroids = [np.mean(sub_cluster, axis=0) for sub_cluster in sub_clusters]
    
    return sub_clusters, centroids

然后，我们定义一个递归函数来分裂聚类，直到满足某个终止条件为止。这里我们使用了层次聚类的轮廓系数来评估聚类效果：

def divisive_clustering(cluster, X, min_size=5, max_depth=10):
    if len(cluster) <= min_size or max_depth == 0:
        return cluster
    
    sub_clusters, centroids = split_cluster(cluster, X)
    
    # Compute the silhouette score of the sub-clusters
    sub_scores = []
    for sub_cluster in sub_clusters:
        sub_scores.append(silhouette_score(sub_cluster, np.full(len(sub_cluster), len(sub_clusters)), metric='euclidean'))
    
    # Find the sub-cluster with the lowest silhouette score
    min_idx = np.argmin(sub_scores)
    
    if sub_scores[min_idx] > silhouette_score(cluster, np.full(len(cluster), 0), metric='euclidean'):
        return cluster
    
    left_cluster = divisive_clustering(sub_clusters[min_idx], X, min_size=min_size, max_depth=max_depth-1)
    right_cluster = divisive_clustering(np.concatenate([sub_clusters[i] for i in range(len(sub_clusters)) if i != min_idx]), X, min_size=min_size, max_depth=max_depth-1)
    
    return [left_cluster, right_cluster]

最后，我们可以使用 `divisive_clustering` 函数对数据进行聚类，并可视化聚类结果：

clusters = divisive_clustering(X, X, min_size=5, max_depth=10)

colors = ['r', 'g', 'b', 'y', 'c', 'm']
color_map = {}
for i, cluster in enumerate(clusters):
    for j in range(len(cluster)):
        color_map[tuple(cluster[j])] = colors[i]

colors = [color_map[tuple(X[i])] for i in range(len(X))]

fig = plt.figure(1)
ax = Axes3D(fig, rect=[0, 0, .95, 1], elev=48, azim=134)
ax.scatter(X[:, 3], X[:, 0], X[:, 2], c=colors, edgecolor='k')
plt.show()

这将生成一个 3D 散点图，其中不同的颜色表示不同的聚类。