New Coresets for Projective Clustering and Applications

• Main Authors: Tukan, Murad, Wu, Xuan, Zhou, Samson, Braverman, Vladimir, Feldman, Dan
• Format: Journal Article
• Language: English
• Published: 08-03-2022
• Subjects: Computer Science - Learning
• DOI: 10.48550/arxiv.2203.04370

$(j,k)$-projective clustering is the natural generalization of the family of
$k$-clustering and $j$-subspace clustering problems. Given a set of points $P$
in $\mathbb{R}^d$, the goal is to find $k$ flats of dimension $j$, i.e., affine
subspaces, that best fit $P$ under a given distance measure. In this paper, we
propose the first algorithm that returns an $L_\infty$ coreset of size
polynomial in $d$. Moreover, we give the first strong coreset construction for
general $M$-estimator regression. Specifically, we show that our construction
provides efficient coreset constructions for Cauchy, Welsch, Huber,
Geman-McClure, Tukey, $L_1-L_2$, and Fair regression, as well as general
concave and power-bounded loss functions. Finally, we provide experimental
results based on real-world datasets, showing the efficacy of our approach.