Large Data Limit of the MBO Scheme for Data Clustering-Reference-Cited by-同舟云学术

Large Data Limit of the MBO Scheme for Data Clustering

Published:2023-03 Issue:1 Volume:22 Page:
ISSN:1617-7061
Container-title:PAMM
language:en
Short-container-title:Proc Appl Math and Mech

Author:

Laux Tim¹,Lelmi Jona¹

Affiliation:

1. Hausdorff Center for Mathematics University of Bonn Villa Maria, Endenicher Allee 62 53115 Bonn Germany

Abstract

AbstractThe MBO scheme is a highly performant scheme used for data clustering and other applications in machine learning. We report on the first theoretical studies of the scheme in the large data limit. Our results relate (i) the final state of the scheme to minimal surfaces in the data manifold and (ii) the dynamics of the scheme to the steepest descent for surfaces, which is mean curvature flow. The tools employed are variational methods for (i) and viscosity solution techniques for (ii).

Publisher

Wiley

Subject

Electrical and Electronic Engineering,Atomic and Molecular Physics, and Optics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.202200308

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1. Large Data Limit of the MBO Scheme for Data Clustering;PAMM;2023-03