no code implementations • 6 Feb 2024 • Yikun Bai, Rocio Diaz Martin, Abihith Kothapalli, Hengrong Du, Xinran Liu, Soheil Kolouri
We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others.
no code implementations • 4 Feb 2024 • Huy Tran, Yikun Bai, Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu, Rocio Diaz Martin, Soheil Kolouri
Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning.
no code implementations • 9 Oct 2023 • Rocio Diaz Martin, Ivan Medri, Yikun Bai, Xinran Liu, Kangbai Yan, Gustavo K. Rohde, Soheil Kolouri
The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning.
1 code implementation • 7 Feb 2023 • Yikun Bai, Ivan Medri, Rocio Diaz Martin, Rana Muhammad Shahroz Khan, Soheil Kolouri
To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed.
no code implementations • 16 Jul 2022 • Sumati Thareja, Gustavo Rohde, Rocio Diaz Martin, Ivan Medri, Akram Aldroubi
The method builds upon signal estimation using the cumulative distribution transform (CDT) originally introduced for positive distributions.
1 code implementation • 3 Jun 2021 • Akram Aldroubi, Rocio Diaz Martin, Ivan Medri, Gustavo K. Rohde, Sumati Thareja
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements.