K-Means Clustering With Incomplete Data with the Use of Mahalanobis Distances

TL;DR

This paper introduces a unified K-means clustering algorithm that uses Mahalanobis distances to better handle incomplete data with elliptical clusters, outperforming existing methods in experiments.

Contribution

The work extends previous unified clustering-imputation approaches by incorporating Mahalanobis distances, improving clustering accuracy for elliptical data shapes.

Findings

Our algorithm outperforms standalone imputation and clustering methods.

It achieves higher ARI and NMI scores on synthetic and real datasets.

Results demonstrate robustness across different data distributions.

Abstract

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.