(Probably) concave graph matching

Haggai Maron; Yaron Lipman

doi:10.48550/arXiv.1807.09722

(Probably) concave graph matching

Haggai Maron, Yaron Lipman

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

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

Abstract

In this paper, we address the graph matching problem. Following the recent works of Zaslavskiy et al. (2009); Vestner et al. (2017) we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and probably conditionally concave energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (e.g., doubly stochastic) are with high probability extreme points of the matching polytope (e.g., permutations).

Original language	English
Pages (from-to)	408-418
Number of pages	11
Journal	Advances in Neural Information Processing Systems
Volume	2018-December
DOIs	https://doi.org/10.48550/arXiv.1807.09722
State	Published - 3 Dec 2018
Event	32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: 2 Dec 2018 → 8 Dec 2018

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

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title = "(Probably) concave graph matching",

abstract = "In this paper, we address the graph matching problem. Following the recent works of Zaslavskiy et al. (2009); Vestner et al. (2017) we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and probably conditionally concave energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (e.g., doubly stochastic) are with high probability extreme points of the matching polytope (e.g., permutations).",

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AU - Lipman, Yaron

PY - 2018/12/3

Y1 - 2018/12/3

N2 - In this paper, we address the graph matching problem. Following the recent works of Zaslavskiy et al. (2009); Vestner et al. (2017) we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and probably conditionally concave energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (e.g., doubly stochastic) are with high probability extreme points of the matching polytope (e.g., permutations).

AB - In this paper, we address the graph matching problem. Following the recent works of Zaslavskiy et al. (2009); Vestner et al. (2017) we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and probably conditionally concave energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (e.g., doubly stochastic) are with high probability extreme points of the matching polytope (e.g., permutations).

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U2 - 10.48550/arXiv.1807.09722

DO - 10.48550/arXiv.1807.09722

M3 - مقالة من مؤنمر

SN - 1049-5258

VL - 2018-December

SP - 408

EP - 418

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018

Y2 - 2 December 2018 through 8 December 2018

ER -

(Probably) concave graph matching

Abstract

All Science Journal Classification (ASJC) codes

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