Fitting a putative manifold to noisy data

Charles Fefferman; Sergei Ivanov; Yaroslav Kurylev; Matti Lassas; Hariharan Narayanan

Fitting a putative manifold to noisy data

Charles Fefferman, Sergei Ivanov, Yaroslav Kurylev, Matti Lassas, Hariharan Narayanan

Mathematics

Princeton University

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

Abstract

In the present work, we give a solution to the following question from manifold learning. Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded manifold M, and corrupted by a small amount of gaussian noise.

Original language	American English
Pages (from-to)	688-720
Number of pages	33
Journal	Proceedings of Machine Learning Research
Volume	75
State	Published - 2018
Event	31st Annual Conference on Learning Theory, COLT 2018 - Stockholm, Sweden Duration: Jul 6 2018 → Jul 9 2018

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Keywords

Hausdorff distance
Manifold learning
reach

Cite this

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title = "Fitting a putative manifold to noisy data",

abstract = "In the present work, we give a solution to the following question from manifold learning. Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded manifold M, and corrupted by a small amount of gaussian noise.",

keywords = "Hausdorff distance, Manifold learning, reach",

author = "Charles Fefferman and Sergei Ivanov and Yaroslav Kurylev and Matti Lassas and Hariharan Narayanan",

note = "Funding Information: Ch.F. was partly supported AFOSR, grant DMS-1265524, and NSF, grant FA9550-12-1-0425. S.I. was partly supported RFBR, grant 14-01-00062, Y.K. was partly supported by EPSRC and the AXA professorship, M.L. was supported by Academy of Finland, grants 273979 and 284715, and H.N. was partly supported by NSF grant DMS-1620102 and a Ramanujan Fellowship. Publisher Copyright: {\textcopyright} 2018 C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas & H. Narayanan.; 31st Annual Conference on Learning Theory, COLT 2018 ; Conference date: 06-07-2018 Through 09-07-2018",

year = "2018",

language = "American English",

volume = "75",

pages = "688--720",

journal = "Proceedings of Machine Learning Research",

issn = "2640-3498",

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TY - JOUR

T1 - Fitting a putative manifold to noisy data

AU - Fefferman, Charles

AU - Ivanov, Sergei

AU - Kurylev, Yaroslav

AU - Lassas, Matti

AU - Narayanan, Hariharan

N1 - Funding Information: Ch.F. was partly supported AFOSR, grant DMS-1265524, and NSF, grant FA9550-12-1-0425. S.I. was partly supported RFBR, grant 14-01-00062, Y.K. was partly supported by EPSRC and the AXA professorship, M.L. was supported by Academy of Finland, grants 273979 and 284715, and H.N. was partly supported by NSF grant DMS-1620102 and a Ramanujan Fellowship. Publisher Copyright: © 2018 C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas & H. Narayanan.

PY - 2018

Y1 - 2018

N2 - In the present work, we give a solution to the following question from manifold learning. Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded manifold M, and corrupted by a small amount of gaussian noise.

AB - In the present work, we give a solution to the following question from manifold learning. Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded manifold M, and corrupted by a small amount of gaussian noise.

KW - Hausdorff distance

KW - Manifold learning

KW - reach

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M3 - Conference article

SN - 2640-3498

VL - 75

SP - 688

EP - 720

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 31st Annual Conference on Learning Theory, COLT 2018

Y2 - 6 July 2018 through 9 July 2018

ER -

Fitting a putative manifold to noisy data

Abstract

ASJC Scopus subject areas

Keywords

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