Local structure alignment guided domain adaptation with few source samples

Domain adaptation has received lots of attention for its high efficiency in dealing with cross-domain learning tasks. Most existing domain adaptation methods adopt the strategies relying on large amounts of source label information, which limits their applications in the real world where only a few label samples are available. We exploit the local geometric connections to tackle this problem and propose a Local Structure Alignment (LSA) guided domain adaptation method in this paper. LSA leverages the Nyström method to describe the distribution difference from the geometric perspective and then perform the distribution alignment between domains. Specifically, LSA constructs a domain-invariant Hessian matrix to locally connect the data of the two domains through minimizing the Nyström approximation error. And then it integrates the domain-invariant Hessian matrix with the semi-supervised learning and finally builds an adaptive semi-supervised model. Extensive experimental results validate that the proposed LSA outperforms the traditional domain adaptation methods especially when only sparse source label information is available.