kmeans 算法中的 Dunn 指数和惯性

Question

我有对某些数据运行 KMeans 算法的代码，但我现在需要它来计算 Dunn 指数和惯性，但由于该程序的限制是 numpy、matplotlib 和 csv，所以没有在线视频显示如何计算 Dunn 指数只有这几个库，我不太喜欢数学，所以将实际的数学应用到代码中对我来说太难了......

我在网上搜索了如何利用 numpy 的限制在 python 中计算 dunn 指数和惯性，但一切都使用了另一个库。

这是代码：

import numpy as np
import matplotlib.pyplot as plt
import csv

def load_data(file_path):
    data = []
    with open(file_path, 'r') as csvfile:
        csvreader = csv.reader(csvfile)
        next(csvreader)
        for row in csvreader:
            data.append([float(row[0]), float(row[1])])
    return np.array(data)

def calculate_distances(data, centers):
    data_with_distances = data.copy()
    num_centers = centers.shape[0]
    
    for i in range(num_centers):
        distances = np.sqrt(((data - centers[i]) ** 2).sum(axis=1))
        data_with_distances = np.column_stack((data_with_distances, distances))
    
    return data_with_distances

def get_clusters(data_with_distances):
    num_clusters = data_with_distances.shape[1] - 2 
    cluster_masks = []
    for i in range(num_clusters):
        mask = data_with_distances[:, i+2] == np.min(data_with_distances[:, 2:num_clusters+2], axis=1)
        cluster_masks.append(mask)
    
    clusters = [data_with_distances[mask, :] for mask in cluster_masks]
    return clusters

def calculate_centers(clusters):
    centers = np.array([cluster.mean(axis=0)[:2] for cluster in clusters])
    return centers

def plot_clusters(clusters, centers):
    colors = ['blue', 'red', 'green']
    for i, cluster in enumerate(clusters):
        plt.scatter(cluster[:, 0], cluster[:, 1], color=colors[i])
    for center in centers:
        plt.scatter(center[0], center[1], color='purple', marker='*', s=150)
    plt.xlabel('Household Total Assets')
    plt.ylabel('Annual Household Income')
    plt.title('K-means Clustering of Household Data')
    plt.show()

def run(data, num_clusters, max_iterations=100):
    current_centers = np.random.permutation(data)[:num_clusters]
    
    for iteration in range(max_iterations):
        data_with_distances = calculate_distances(data, current_centers)
        clusters = get_clusters(data_with_distances)
        current_centers = calculate_centers(clusters)

    plot_clusters(clusters, current_centers)
    
def main(file_path):
    data = load_data(file_path)
    for num_clusters in range(2, 11):
        run(data, num_clusters)

file_path = 'assessment2dmv.csv'
num_clusters = 3
main(file_path)

Answer 1

对于 dunn 索引，您可以使用 this github repo，您可以在其中找到以下函数：

def dunn(k_list):
    """ Dunn index [CVI]
    
    Parameters
    ----------
    k_list : list of np.arrays
        A list containing a numpy array for each cluster |c| = number of clusters
        c[K] is np.array([N, p]) (N : number of samples in cluster K, p : sample dimension)
    """
    deltas = np.ones([len(k_list), len(k_list)])*1000000
    big_deltas = np.zeros([len(k_list), 1])
    l_range = list(range(0, len(k_list)))
    
    for k in l_range:
        for l in (l_range[0:k]+l_range[k+1:]):
            deltas[k, l] = delta(k_list[k], k_list[l])
        
        big_deltas[k] = big_delta(k_list[k])

    di = np.min(deltas)/np.max(big_deltas)
    return di

关于惯性，您需要计算（x 是簇 k 的向量，mu 是簇 k 的中心）：

代码看起来像这样：

def get_inertia(clusters, centers)
    J=0
    for center in centers :
        for cluster in clusters :
            J+=(cluster - center)**2
    return J