Diffusion Transportation Cost for Domain Adaptation
Keywords: Optimal Transport, Domain Adaptation, Diffusion geometry, Manifold learning, Kernel methods, Riemannian manifolds.
TL;DR: Introducing Diffusion-OT, a transportation cost for optimal transport in domain adaptation, which incorporates intra-domain relationships using diffusion geometry.
Abstract: In recent years, there has been considerable interest in leveraging the Optimal Transport (OT) problem for domain adaptation, a strategy shown to be highly effective.
However, a less explored aspect is the choice of the transportation cost function, as most existing methods rely on the pairwise squared Euclidean distances for the transportation cost, potentially overlooking important intra-domain geometries.
This paper presents Diffusion-OT, a new transport cost for the OT problem, designed specifically for domain adaptation. By utilizing concepts and tools from the field of manifold learning, specifically diffusion geometry, we derive an operator that accounts for the intra-domain relationships, thereby 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 transportation cost.
We provide proof that the proposed operator is in fact a diffusion operator, demonstrating that the cost function is defined by an anisotropic diffusion process between the domains.
In addition, to enhance performance, we integrate source labels into the operator, thereby guiding the anisotropic diffusion according to the classes.
We showcase the effectiveness of Diffusion-OT through comprehensive experiments, demonstrating its superior performance compared to recent methods across various benchmarks and datasets.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 7570
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