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.
|Number of pages||27|
|Journal||Proceedings of Machine Learning Research|
|State||Published - 2023|
|Event||40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States|
Duration: 23 Jul 2023 → 29 Jul 2023
Bibliographical notePublisher Copyright:
© 2023 Proceedings of Machine Learning Research. All rights reserved.
ASJC Scopus subject areas
- Artificial Intelligence
- Control and Systems Engineering
- Statistics and Probability