实现聚类性能指标DBI, DI, CHI, SI

聚类性能指标是用于评估聚类算法聚类效果的指标，常见的有DBI、DI、CHI、SI等。

以下是这四个指标的实现方法：

（1）DBI（Davies-Bouldin Index）：DBI指标越小，说明聚类效果越好。DBI指标的计算方法如下：

import numpy as np
from sklearn.metrics.pairwise import euclidean_distances

def compute_centroids(X, labels):
    k = np.max(labels) + 1
    centroids = np.zeros((k, X.shape[1]))
    for i in range(k):
        centroids[i] = np.mean(X[labels == i], axis=0)
    return centroids

def compute_S(X, labels, centroids):
    k = np.max(labels) + 1
    S = np.zeros(k)
    for i in range(k):
        S[i] = np.mean(euclidean_distances(X[labels == i], [centroids[i]]))
    return S

def compute_R(X, labels, centroids):
    k = np.max(labels) + 1
    R = np.zeros((k, k))
    for i in range(k):
        for j in range(k):
            if i != j:
                R[i][j] = (S[i] + S[j]) / euclidean_distances([centroids[i]], [centroids[j]])
    return R

def compute_DBI(X, labels):
    k = np.max(labels) + 1
    centroids = compute_centroids(X, labels)
    S = compute_S(X, labels, centroids)
    R = compute_R(X, labels, centroids)
    DBI = 0.0
    for i in range(k):
        max_R = np.max(R[i, [j for j in range(k) if j != i]])
        DBI += max_R + S[i]
    return DBI / k

（2）DI（Dunn Index）：DI指标越大，说明聚类效果越好。DI指标的计算方法如下：

import numpy as np
from sklearn.metrics.pairwise import euclidean_distances

def compute_min_intercluster_distances(X, labels):
    k = np.max(labels) + 1
    min_intercluster_distances = np.full((k, k), np.inf)
    for i in range(k):
        for j in range(i + 1, k):
            dist = np.min(euclidean_distances(X[labels == i], X[labels == j]))
            min_intercluster_distances[i][j] = dist
            min_intercluster_distances[j][i] = dist
    return min_intercluster_distances

def compute_max_intracluster_diameter(X, labels):
    k = np.max(labels) + 1
    max_intracluster_diameter = np.zeros(k)
    for i in range(k):
        dist = euclidean_distances(X[labels == i])
        max_intracluster_diameter[i] = np.max(dist) if len(dist) > 0 else 0
    return max_intracluster_diameter

def compute_DI(X, labels):
    min_intercluster_distances = compute_min_intercluster_distances(X, labels)
    max_intracluster_diameter = compute_max_intracluster_diameter(X, labels)
    DI = np.min(min_intercluster_distances) / np.max(max_intracluster_diameter)
    return DI

（3）CHI（Calinski-Harabasz Index）：CHI指标越大，说明聚类效果越好。CHI指标的计算方法如下：

import numpy as np
from sklearn.metrics.pairwise import euclidean_distances

def compute_centroids(X, labels):
    k = np.max(labels) + 1
    centroids = np.zeros((k, X.shape[1]))
    for i in range(k):
        centroids[i] = np.mean(X[labels == i], axis=0)
    return centroids

def compute_SSB(X, labels, centroids):
    k = np.max(labels) + 1
    SSB = 0.0
    overall_centroid = np.mean(X, axis=0)
    for i in range(k):
        n = len(X[labels == i])
        SSB += n * euclidean_distances([centroids[i]], [overall_centroid])
    return SSB

def compute_SSW(X, labels, centroids):
    k = np.max(labels) + 1
    SSW = 0.0
    for i in range(k):
        SSW += np.sum(euclidean_distances(X[labels == i], [centroids[i]]) ** 2)
    return SSW

def compute_CHI(X, labels):
    k = np.max(labels) + 1
    centroids = compute_centroids(X, labels)
    SSB = compute_SSB(X, labels, centroids)
    SSW = compute_SSW(X, labels, centroids)
    CHI = (SSB / (k - 1)) / (SSW / (len(X) - k))
    return CHI

（4）SI（Silhouette Index）：SI指标越大，说明聚类效果越好。SI指标的计算方法如下：

import numpy as np
from sklearn.metrics.pairwise import euclidean_distances

def compute_a(X, i, labels):
    a = np.mean(euclidean_distances(X[i], X[labels == labels[i]]))
    return a

def compute_b(X, i, labels):
    k = np.max(labels) + 1
    b = np.inf
    for j in range(k):
        if j != labels[i]:
            dist = np.mean(euclidean_distances(X[i], X[labels == j]))
            if dist < b:
                b = dist
    return b

def compute_SI(X, labels):
    a = np.zeros(len(X))
    b = np.zeros(len(X))
    for i in range(len(X)):
        a[i] = compute_a(X, i, labels)
        b[i] = compute_b(X, i, labels)
    SI = np.mean((b - a) / np.maximum(a, b))
    return SI

以上就是DBI、DI、CHI、SI指标的Python实现方法，可以根据需要选择其中一个或多个指标来评估聚类效果。