Geometric Optimal Transport for Unsupervised Domain Adaptation

TMLR Paper5202 Authors

Abstract:

Optimal Transport (OT) is a widely used and powerful approach in domain adaptation.
While effective, most existing methods rely on the pairwise squared Euclidean distances for the transportation cost, implicitly assuming a Euclidean space.
In this paper, we challenge this assumption by introducing Geometric Optimal Transport (GOT), a new transport cost designed for domain adaptation under the manifold assumption.
By utilizing concepts and tools from the field of manifold learning, specifically diffusion geometry, we derive an operator that accounts for the intra-domain geometries, extending beyond the conventional inter-domain distances.
This operator, which quantifies the probability of transporting between source and target samples, forms the basis for our cost.
We demonstrate how the proposed cost, defined by an anisotropic diffusion process, naturally aligns with the desired properties for domain adaptation.
To further enhance performance, we integrate source labels into the operator, thereby guiding the anisotropic diffusion according to the classes.
We showcase the effectiveness of GOT through comprehensive experiments, demonstrating its superior performance compared to recent methods across various benchmarks and datasets.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Rémi_Flamary1

Submission Number: 5202