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

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arxiv 1612.07516 v3 pith:TIWDDJKP submitted 2016-12-22 cs.LG cs.DS

Johannes Blömer , Sascha Brauer , Kathrin Bujna This is my paper · ORCID
classification cs.LGcs.DS
keywords meansfuzzycoresetsproblemnumberpointsapproximationarrive
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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.

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