This paper introduces a learning scheme to construct a Hilbert space (i.e., a vector space along its inner product) to address both unsupervised and semi-supervised domain adaptation problems. This is achieved by learning projections from each domain to a latent space along the Mahalanobis metric of the latent space to simultaneously minimizing a notion of domain variance while maximizing a measure of discriminatory power. In particular, we make use of the Riemannian optimization techniques to match statistical properties (e.g., first and second order statistics) between samples projected into the latent space from different domains. Upon availability of class labels, we further deem samples sharing the same label to form more compact clusters while pulling away samples coming from different classes.We extensively evaluate and contrast our proposal against state-of-the-art methods for the task of visual domain adaptation using both handcrafted and deep-net features. Our experiments show that even with a simple nearest neighbor classifier, the proposed method can outperform several state-of-the-art methods benefitting from more involved classification schemes.
@cite_7 observed that the geodesic connecting the source and target subspaces conveys useful information for DA and proposed the Sampling Geodesic Flow (SGF) method . The Geodesic Flow Kernel (GFK) is an improvement over the SGF technique where instead of sampling a few points on the geodesic, the whole curve is used for domain adaptation . In both methods, the domain subspaces are fixed and obtained by Principal Component Analysis (PCA) or Partial Least Square regression (PLS) . In contrast to our solution, in SGF and GFK learning the domain subspaces is disjoint from the knowledge transfer algorithm. In our experiments, we will see that the subspaces determined by our method can even boost the performance of GFK, showing the importance of joint learning of domain subspaces and the knowledge transfer scheme. @cite_23 dictionary learning is used for interpolating the intermediate subspaces.
@cite_23 @cite_7
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Domain adaptation addresses the problem where data instances of a source domain have different distributions from that of a target domain, which occurs frequently in many real life scenarios. This work focuses on unsupervised domain adaptation, where labeled data are only available in the source domain. We propose to interpolate subspaces through dictionary learning to link the source and target domains. These subspaces are able to capture the intrinsic domain shift and form a shared feature representation for cross domain recognition. Further, we introduce a quantitative measure to characterize the shift between two domains, which enables us to select the optimal domain to adapt to the given multiple source domains. We present experiments on face recognition across pose, illumination and blur variations, cross dataset object recognition, and report improved performance over the state of the art. Adapting the classifier trained on a source domain to recognize instances from a new target domain is an important problem that is receiving recent attention. In this paper, we present one of the first studies on unsupervised domain adaptation in the context of object recognition, where we have labeled data only from the source domain (and therefore do not have correspondences between object categories across domains). Motivated by incremental learning, we create intermediate representations of data between the two domains by viewing the generative subspaces (of same dimension) created from these domains as points on the Grassmann manifold, and sampling points along the geodesic between them to obtain subspaces that provide a meaningful description of the underlying domain shift. We then obtain the projections of labeled source domain data onto these subspaces, from which a discriminative classifier is learnt to classify projected data from the target domain. We discuss extensions of our approach for semi-supervised adaptation, and for cases with multiple source and target domains, and report competitive results on standard datasets.