如何使用Python编写一个用于评估聚类问题性能的常用指标代码？

在Python中，评估聚类问题性能常用的指标有轮廓系数（Silhouette Coefficient）、Calinski-Harabasz指数和Davies-Bouldin指数等。下面分别给出这些指标的计算方法。

**1. 轮廓系数（Silhouette Coefficient）**

from sklearn.metrics import silhouette_score
import numpy as np

def silhouette_coefficient(y_true, y_pred):
    return silhouette_score(np.array(y_true), np.array(y_pred))

# 使用法：y_true是真实标签，y_pred是预测的聚类标签
silhouette = silhouette_coefficient(y_true, y_pred)

**2. Calinski-Harabasz指数**

from scipy.spatial.distance import cdist
from scipy.stats import chi2
from sklearn.metrics.pairwise import pairwise_distances_argmin_min

def calinski_harabasz_score(X, labels):
    n_samples, _ = X.shape
    n_clusters = len(set(labels))  # unique cluster numbers
    intra_sum_of_squares = sum(cdist(X[labels == i], X[labels == i], 'euclidean') ** 2 for i in range(n_clusters))
    tot_sum_of_squares = sum((X - X.mean(axis=0)) ** 2, axis=1).sum()
    return n_clusters * (tot_sum_of_squares / intra_sum_of_squares)

# 使用法：X是特征矩阵，labels是聚类标签
calinski.harabasz_score(X, labels)

**3. Davies-Bouldin指数**

from scipy.spatial.distance import squareform, pdist
from math import sqrt

def davies_bouldin_index(X, labels):
    dists = squareform(pdist(X, metric='euclidean'))
    sums_of_squares_within = []
    sums_of_squares_between = []
    
    for i in range(len(set(labels))):
        cluster_members = X[labels == i]
        mean_centroid = cluster_members.mean(axis=0)
        within_SS = sum((x - mean_centroid)**2 for x in cluster_members)
        between_SS = 0
        for j in range(i + 1, len(set(labels))):
            centroid_j = X[labels == j].mean(axis=0)
            diff = abs(mean_centroid - centroid_j)
            between_SS += sum(dists[i][k] + dists[k][j] for k in range(len(cluster_members)))
        sums_of_squares_between.append(between_SS / len(cluster_members))
        sums_of_squares_within.append(within_SS)
        
    DBI = max(sums_of_squares_within) / min(sums_of_squares_between)
    return DBI

# 使用法同上
davies_bouldin_index(X, labels)