用马氏距离统一处理缺失数据的K均值聚类,效果更优。
K-Means Clustering With Incomplete Data with the Use of Mahalanobis Distances
- 将聚类与数据补全结合,用马氏距离替代欧氏距离
- 在椭圆簇数据上,调整兰德指数和互信息均更高
- 适合处理形状不规则、有缺失值的数据集
将缺失特征的聚类任务中有效应用K均值算法仍是一个重要研究方向,因其对现实应用具有深远影响。近期研究表明,将K均值聚类与数据补全统一为单一目标函数并联合求解,相比分别处理补全与聚类更具优势。本文在此基础上,提出一种融合马氏距离的统一K均值算法,取代传统欧氏距离,因马氏距离在椭圆形状簇上表现更佳。我们在包含最多十个椭圆簇的合成数据集以及IRIS数据集上进行了大量实验。通过调整兰德指数(ARI)和归一化互信息(NMI)评估,结果表明该算法在所有测试场景中均优于独立进行数据补全后接K均值(使用马氏或欧氏距离)以及现有集成式缺损数据K均值算法。这些优势在IRIS数据集和随机生成的椭圆簇数据上均持续显著。
原文摘要 · Abstract (English)
Effectively applying the K-means algorithm to clustering tasks with incomplete features remains an important research area due to its impact on real-world applications. Recent work has shown that unifying K-means clustering and imputation into one single objective function and solving the resultant optimization yield superior results compared to handling imputation and clustering separately. In this work, we extend this approach by developing a unified K-means algorithm that incorporates Mahalanobis distances, instead of the traditional Euclidean distances, which previous research has shown to perform better for clusters with elliptical shapes. We conducted extensive experiments on synthetic datasets containing up to ten elliptical clusters, as well as the IRIS dataset. Using the Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI), we demonstrate that our algorithm consistently outperforms both standalone imputation followed by K-means (using either Mahalanobis or Euclidean distance) and K-Means with Incomplete Data, the recent K-means algorithms that integrate imputation and clustering for handling incomplete data. These results hold across both the IRIS dataset and randomly generated data with elliptical clusters.
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