Subspace Alignment For Domain Adaptation

In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces spanned by eigenvectors. Our method seeks a domain invariant feature space by learning a mapping function which aligns the source subspace with the target one. We show that the solution of the corresponding optimization problem can be ob-tained in a simple closed form, leading to an extremely fast algorithm. We present two approaches to determine the only hyper-parameter in our method corresponding to the size of the subspaces. In the first approach we tune the size of subspaces using a theoretical bound on the stability of the obtained result. In the second ap-proach, we use maximum likelihood estimation to de-termine the subspace size, which is particularly useful for high dimensional data. Apart from PCA, we pro-pose a subspace creation method that outperform par-tial least squares (PLS) and linear discriminant analysis (LDA) in domain adaptation. We test our method on various datasets and show that, despite its intrinsic sim-plicity, it outperforms state of the art DA methods.