实现聚类性能指标dbi,di, chi

以下是计算聚类性能指标 Davies-Bouldin Index (DBI)，Dunn Index (DI) 和 Calinski-Harabasz Index (CHI) 的 Python 代码示例：

from sklearn.cluster import KMeans
from sklearn.metrics import pairwise_distances
from sklearn.datasets import make_blobs
import numpy as np

# 生成随机数据集
X, y = make_blobs(n_samples=300, centers=4, cluster_std=0.6, random_state=0)

# 计算聚类中心和标签
kmeans = KMeans(n_clusters=4, random_state=0).fit(X)
labels = kmeans.labels_
centers = kmeans.cluster_centers_

# 计算聚类内部的平均距离和聚类间的距离
avg_distances = np.zeros(len(centers))
for i, center in enumerate(centers):
    avg_distances[i] = np.mean(pairwise_distances(X[labels == i], [center]))

inter_distances = pairwise_distances(centers)

# 计算 DBI
dbi = 0
for i in range(len(centers)):
    max_ratio = -np.inf
    for j in range(len(centers)):
        if i != j:
            ratio = (avg_distances[i] + avg_distances[j]) / inter_distances[i][j]
            if ratio > max_ratio:
                max_ratio = ratio
    dbi += max_ratio

dbi /= len(centers)
print("DBI:", dbi)

# 计算 DI
di = np.inf
for i in range(len(centers)):
    for j in range(len(centers)):
        if i != j:
            ratio = inter_distances[i][j] / max(avg_distances[i], avg_distances[j])
            if ratio < di:
                di = ratio

print("DI:", di)

# 计算 CHI
chi = np.trace(inter_distances) / np.trace(np.cov(X.T)) * (len(X) - len(centers)) / (len(centers) - 1)
print("CHI:", chi)

其中，`make_blobs` 用于生成随机数据集，`KMeans` 用于聚类，`pairwise_distances` 用于计算距离矩阵，最终输出 DBI、DI 和 CHI 的值。