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.
Data representation with optimal transport
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abstract
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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Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
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.