Provable Imbalanced Point Clustering

David Denisov, Dan Feldman, Shlomi Dolev, Michael Segal

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 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 \(1\pm \varepsilon \). In Sect. 3 we provide 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.