New Coresets for Projective Clustering and Applications

• URL: http://arxiv.org/abs/2203.04370v1
• Date: Tue, 8 Mar 2022 19:50:27 GMT
• Title: New Coresets for Projective Clustering and Applications
• Authors: Murad Tukan and Xuan Wu and Samson Zhou and Vladimir Braverman and Dan Feldman
• Abstract summary: Given a set of points $P$ in $mathbbRd$, the goal is to find $k$ flats of dimension $j$, i.e., affine subspaces, that best fit $P$ under a given distance measure. We show that our construction provides efficient coreset constructions for Cauchy, Welsch, Huber, Geman-McClure, Tukey, $L_infty$, and Fair regression.
• Score: 34.82221047030618
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: $(j,k)$-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.

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