Hierarchical Representation for Multi-Source Domain Adaptation via Wasserstein Barycenter

This work addresses the problem of multi-source domain adaptation using the Wasserstein barycenter through a hierarchical data representation. Most current approaches tackle this problem by treating each source domain as a probability measure whose support comprises its data points. In this paper, we offer a new perspective: we conceptualize a source domain as a probability measure whose support includes its classes, with each class treated as a separate probability measure, and its support is formed by the points belonging to it. Our method, called Wasserstein Barycenter for Hierarchical Representation (WBHR), aims at constructing an auxiliary source domain formed by aggregated classes sharing the same label within different domains, using the Wasserstein barycenter, thereby transforming the problem into a standard single-source adaptation task, which is addressed through hierarchical optimal transport. We discuss the theoretical aspects of the method and propose a conceptually simple algorithm. Empirical evaluations demonstrate that our WBHR model outperforms existing multi-source domain adaptation techniques across two benchmark datasets, underscoring its efficacy for practical applications.