New Coresets for Projective Clustering and Applications

Murad Tukan, Xuan Wu, Samson Zhou, Vladimir Braverman, Dan Feldman

Research output: Contribution to journalConference articlepeer-review


(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 Rd, 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 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, L1 − L2, 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.

Original languageEnglish
Pages (from-to)5391-5415
Number of pages25
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain
Duration: 28 Mar 202230 Mar 2022

Bibliographical note

Publisher Copyright:
Copyright © 2022 by the author(s)

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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