New Coresets for Projective Clustering and Applications

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

New Coresets for Projective Clustering and Applications

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

Department of Computer Science

Research output: Contribution to journal › Conference article › peer-review

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 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_∞ 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 language	English
Pages (from-to)	5391-5415
Number of pages	25
Journal	Proceedings of Machine Learning Research
Volume	151
State	Published - 2022
Event	25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain Duration: 28 Mar 2022 → 30 Mar 2022

Bibliographical note

Funding Information:
This research was partially supported by the Israel National Cyber Directorate via the BIU Center for Applied Research in Cyber Security, and supported in part by NSF CAREER grant 1652257, NSF grant 1934979, ONR Award N00014-18-1-2364 and the Lifelong Learning Machines program from DARPA/MTO. In addition, Samson Zhou would like to thank National Institute of Health grant 5401 HG 10798-2 and a Simons Investigator Award of David P. Woodruff.

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

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Cite this

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title = "New Coresets for Projective Clustering and Applications",

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 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.",

author = "Murad Tukan and Xuan Wu and Samson Zhou and Vladimir Braverman and Dan Feldman",

note = "Funding Information: This research was partially supported by the Israel National Cyber Directorate via the BIU Center for Applied Research in Cyber Security, and supported in part by NSF CAREER grant 1652257, NSF grant 1934979, ONR Award N00014-18-1-2364 and the Lifelong Learning Machines program from DARPA/MTO. In addition, Samson Zhou would like to thank National Institute of Health grant 5401 HG 10798-2 and a Simons Investigator Award of David P. Woodruff. Publisher Copyright: Copyright {\textcopyright} 2022 by the author(s); 25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 ; Conference date: 28-03-2022 Through 30-03-2022",

year = "2022",

language = "English",

volume = "151",

pages = "5391--5415",

journal = "Proceedings of Machine Learning Research",

issn = "2640-3498",

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T1 - New Coresets for Projective Clustering and Applications

AU - Tukan, Murad

AU - Wu, Xuan

AU - Zhou, Samson

AU - Braverman, Vladimir

AU - Feldman, Dan

N1 - Funding Information: This research was partially supported by the Israel National Cyber Directorate via the BIU Center for Applied Research in Cyber Security, and supported in part by NSF CAREER grant 1652257, NSF grant 1934979, ONR Award N00014-18-1-2364 and the Lifelong Learning Machines program from DARPA/MTO. In addition, Samson Zhou would like to thank National Institute of Health grant 5401 HG 10798-2 and a Simons Investigator Award of David P. Woodruff. Publisher Copyright: Copyright © 2022 by the author(s)

PY - 2022

Y1 - 2022

N2 - (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.

AB - (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.

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M3 - Conference article

AN - SCOPUS:85163099676

SN - 2640-3498

VL - 151

SP - 5391

EP - 5415

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022

Y2 - 28 March 2022 through 30 March 2022

ER -

New Coresets for Projective Clustering and Applications

Abstract

Bibliographical note

ASJC Scopus subject areas

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