Domain Adaptation with Optimal Transport for Extended Variable Space

Domain adaptation aims to transfer knowledge of labeled instances obtained from a source domain to a target domain to fill the gap between the domains. Most domain adaptation methods assume that the source and target domains have the same dimensionality. Methods that are applicable when the number of features for each sample is different in each domain have rarely been studied, especially when no label information is given for the test data obtained from the target domain. In this paper, it is assumed that common features exist in both domains and that extra (new additional) features are observed in the target domain; hence, the dimensionality of the target domain is higher than that of the source domain. To leverage the homogeneity of the common features, the adaptation between the source and target domains is formulated as an optimal transport (OT) problem. In addition, a learning bound in the target domain for the proposed OT-based method is derived. The experiments with simulated and real-world data show that our proposed algorithm is able to obtain better model for the target domain by considering the extra features given for the target domain.