Clustering with Label Consistency

TL;DR

This paper introduces the concept of label consistency in metric clustering, emphasizing stable point labels, and proposes new algorithms for k-center and k-median problems that prioritize label stability.

Contribution

It defines a new measure of label consistency and develops approximation algorithms for classical clustering problems that incorporate this stability criterion.

Findings

Proposes a new notion of label consistency in clustering.

Designs approximation algorithms for k-center and k-median with label stability.

Addresses the gap between traditional cluster stability and label stability.

Abstract

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.