Label-consistent clustering for evolving data

TL;DR

This paper introduces algorithms for evolving clustering solutions that balance minimizing clustering cost with maintaining consistency with previous solutions, specifically for the $k$-center problem, supported by theoretical and experimental results.

Contribution

It proposes two constant-factor approximation algorithms for label-consistent $k$-center clustering, addressing the challenge of evolving solutions with minimal changes.

Findings

Algorithms achieve constant-factor approximation guarantees.

Experimental results demonstrate effectiveness on real-world data.

Methods successfully balance clustering quality and solution stability.

Abstract

Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information. In addition to seeking a high-quality solution for the task at hand, it is also crucial to ensure consistency by minimizing drastic changes from previous solutions. Applying this approach across many iterations, ensures that the solution evolves gradually and smoothly. In this paper, we study the above problem in the context of clustering, specifically focusing on the $k$-center problem. More precisely, we study the following problem: Given a set of points $X$, parameters $k$ and $b$, and a prior clustering solution $H$ for $X$, our goal is to compute a new solution $C$ for $X$, consisting of $k$ centers, which minimizes the clustering cost while introducing at most $b$ changes from $H$. We refer to this problem as label-consistent $k$-center, and we propose two constant-factor approximation algorithms for it. We complement our theoretical findings with an experimental evaluation demonstrating the effectiveness of our methods on real-world datasets.