Structural Domain Adaptation with Latent Graph Alignment

Domain adaptation aims to transfer knowledge across different data domains (distributions). In this paper, we propose a novel model to enforce the distributional and structural similarities during the adaptation. Specifically, we embed the data from both domain into a latent space where the distributions are matched via minimization of the maximum mean discrepancy metric. Then we characterize the transformed manifold by means of graphs and maximize the similarities between the graphical structure in the embedding space. This is achieved by minimizing the spectrum distance of the graph Laplacians between the embeddings. The spectrum maintains intrinsic information of the manifold and is invariant under data permutations and unitary transformations of the eigenspace. A two stage optimization algorithm is proposed to minimize the distributional and structural differences iteratively. Extensive numerical experiments have been done and demonstrated the superiority of our proposed model over previous arts.