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Data representation with optimal transport

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arxiv 2406.15503 v1 pith:C3AYE2V5 submitted 2024-06-19 math.OC

Rocío Díaz Martín , Ivan V. Medri , Gustavo Kunde Rohde This is my paper · ORCID
classification math.OC
keywords dataoptimaltransportadvancesapplicationsbeenbijectivebriefly
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Optimal transport has been used to define bijective nonlinear transforms and different transport-related metrics for discriminating data and signals. Here we briefly describe the advances in this topic with the main applications and properties in each case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reduced Order Modeling of One-Dimensional Conservative PDEs via the Cumulative Distribution Transform

    math.AP 2026-07 conditional novelty 6.0 of 10

    Mapping solution snapshots to mass-coordinate (CDT) space before POD compresses transport-dominated 1D conservative PDEs into far fewer modes, with proven Kolmogorov-width bounds.

  2. Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification

    math.NA 2025-06 conditional novelty 6.0 of 10

    The paper proves stability bounds for the max-normalized R-CDT under Wasserstein-infinity perturbations and introduces a mean-normalized R-CDT with Wasserstein-2 robustness guarantees for affinely transformed image classes.

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