Efficient Graph Field Integrators Meet Point Clouds

Krzysztof Choromanski; Arijit Sehanobish; Han Lin; Yunfan Zhao; Eli Berger; Tetiana Parshakova; Alvin Pan; David Watkins; Tianyi Zhang; Valerii Likhosherstov; Somnath Basu Roy Chowdhury; Avinava Dubey; Deepali Jain; Tamas Sarlos; Snigdha Chaturvedi; Adrian Weller

Efficient Graph Field Integrators Meet Point Clouds

Krzysztof Choromanski, Arijit Sehanobish, Han Lin, Yunfan Zhao, Eli Berger, Tetiana Parshakova, Alvin Pan, David Watkins, Tianyi Zhang, Valerii Likhosherstov, Somnath Basu Roy Chowdhury, Avinava Dubey, Deepali Jain, Tamas Sarlos, Snigdha Chaturvedi, Adrian Weller

Department of Mathematics

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

Abstract

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion (RFD), uses popular ϵ-nearestneighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs, Greengard & Rokhlin, 1987), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Original language	English
Pages (from-to)	5978-6004
Number of pages	27
Journal	Proceedings of Machine Learning Research
Volume	202
State	Published - 2023
Event	40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States Duration: 23 Jul 2023 → 29 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023 Proceedings of Machine Learning Research. All rights reserved.

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Cite this

@article{8f492c4e55c94c2dbf3790aaca0085f1,

title = "Efficient Graph Field Integrators Meet Point Clouds",

abstract = "We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion (RFD), uses popular ϵ-nearestneighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs, Greengard & Rokhlin, 1987), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.",

author = "Krzysztof Choromanski and Arijit Sehanobish and Han Lin and Yunfan Zhao and Eli Berger and Tetiana Parshakova and Alvin Pan and David Watkins and Tianyi Zhang and Valerii Likhosherstov and Chowdhury, {Somnath Basu Roy} and Avinava Dubey and Deepali Jain and Tamas Sarlos and Snigdha Chaturvedi and Adrian Weller",

note = "Publisher Copyright: {\textcopyright} 2023 Proceedings of Machine Learning Research. All rights reserved.; 40th International Conference on Machine Learning, ICML 2023 ; Conference date: 23-07-2023 Through 29-07-2023",

year = "2023",

language = "English",

volume = "202",

pages = "5978--6004",

journal = "Proceedings of Machine Learning Research",

issn = "2640-3498",

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TY - JOUR

T1 - Efficient Graph Field Integrators Meet Point Clouds

AU - Choromanski, Krzysztof

AU - Sehanobish, Arijit

AU - Lin, Han

AU - Zhao, Yunfan

AU - Berger, Eli

AU - Parshakova, Tetiana

AU - Pan, Alvin

AU - Watkins, David

AU - Zhang, Tianyi

AU - Likhosherstov, Valerii

AU - Chowdhury, Somnath Basu Roy

AU - Dubey, Avinava

AU - Jain, Deepali

AU - Sarlos, Tamas

AU - Chaturvedi, Snigdha

AU - Weller, Adrian

PY - 2023

Y1 - 2023

N2 - We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion (RFD), uses popular ϵ-nearestneighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs, Greengard & Rokhlin, 1987), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

AB - We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion (RFD), uses popular ϵ-nearestneighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs, Greengard & Rokhlin, 1987), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

UR - http://www.scopus.com/inward/record.url?scp=85174397549&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85174397549

SN - 2640-3498

VL - 202

SP - 5978

EP - 6004

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 40th International Conference on Machine Learning, ICML 2023

Y2 - 23 July 2023 through 29 July 2023

ER -

Efficient Graph Field Integrators Meet Point Clouds

Abstract

Bibliographical note

ASJC Scopus subject areas

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