On Coreset Constructions for the Fuzzy $K$-Means Problem

TL;DR

This paper introduces the first coresets for fuzzy K-means clustering that are efficient in size and can be used to compute near-optimal solutions, even in streaming data scenarios.

Contribution

It presents novel coresets for fuzzy K-means with size bounds and demonstrates their use in approximation algorithms and streaming settings.

Findings

Coresets have size linear in dimension and polynomial in clusters.

They enable $(1+\epsilon)$-approximate solutions for fuzzy K-means.

Coresets can be maintained in streaming data environments.

Abstract

The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and poly-logarithmic in the number of points. We show that these coresets can be employed in the computation of a $(1+\epsilon)$-approximation for fuzzy $K$-means, improving previously presented results. We further show that our coresets can be maintained in an insertion-only streaming setting, where data points arrive one-by-one.