Unbalanced Co-relational Optimal Transport for Robust Heterogeneous Data Alignment

Domain adaptation aims to align the data scattered in different domains, which is important for developing generalizable machine learning models. However, real-world data in different domains are often heterogeneous, requiring alignment at both sample and feature levels. In this study, we develop a new optimal transport-based method, unbalanced co-relational optimal transport (UCROT), to achieve robust heterogeneous data alignment. Given the data in different domains, we define a co-relational optimal transport problem, jointly inferring the optimal transport (OT) plans defined at the sample and feature levels. The OT plans indicate the sample correspondence and feature correlation across different domains. In addition, we relax the doubly stochastic constraints of the OT plans to the KL-divergence regularization of their marginals, which enhances the robustness of our method to the sample- and feature-level outliers and leads to the proposed UCROT method. Experiments on the heterogeneous domain adaptation and co-clustering tasks demonstrate the superiority of UCROT.