Provable Imbalanced Point Clustering

Abstract

We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in ${\mathbb{R}}^d$, for any $d,k\ge 1$. To this end, we utilize \emph{coresets}, which, in the context of the paper, are essentially weighted sets of points in ${\mathbb{R}}^d$ that approximate the fitting loss for every model in a given set, up to a multiplicative factor of $1\pm \epsilon$. We provide [Section 3 and Section E in the appendix] experiments that show the empirical contribution of our suggested methods for real images (novel and reference), synthetic data, and real-world data. We also propose choice clustering, which by combining clustering algorithms yields better performance than each one separately.