No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds

TL;DR

This paper introduces a novel constrained k-means clustering method that enforces a maximum radius on clusters to improve robustness against dataset imbalances and sampling artifacts, using semi-definite programming.

Contribution

It presents the first k-means variant with hard radius constraints, formulated via semi-definite programming and quadratic assignment, enhancing robustness in real-world data scenarios.

Findings

Method is robust to dataset imbalances

Effective against sampling artifacts

First to incorporate hard radius constraints in k-means

Abstract

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for visualization or summarization of a dataset. Real world datasets often contain inherent abnormalities, e.g., repeated samples and sampling bias, that manifest imbalanced clustering. We propose to remedy such a scenario by introducing a maximal radius constraint $r$ on the clusters formed by the centroids, i.e., samples from the same cluster should not be more than $2r$ apart in terms of $\ell_2$ distance. We achieve this constraint by solving a semi-definite program, followed by a linear assignment problem with quadratic constraints. Through qualitative results, we show that our proposed method is robust towards dataset imbalances and sampling artifacts. To the best of our knowledge, ours is the first constrained k-means clustering method with hard radius constraints. Codes at https://bit.ly/kmeans-constrained