Lie group manifold analysis: an unsupervised domain adaptation approach for image classification

Domain adaptation aims to minimize the mismatch between the source domain in which models are trained and the target domain to which those models are applied. Most existing works focus on instance reweighting, feature representation, and classifier learning independently, which are ineffective when the domain discrepancy is substantially large. In this study, we propose a new unified hybrid approach that takes advantage of Lie group theory, weighted distribution alignment, and manifold alignment, which are referred to as Lie Group Manifold Analysis (LGMA). LGMA mainly finds a one-parameter sub-group decided by the Lie algebra elements of the intrinsic mean of all samples, and this one-parameter sub-group is a geodesic on the original Lie group. Moreover, the Lie group samples are projected onto the geodesics to maximize the separability of the projected samples for realizing discrimination in the nonlinear Lie group manifold space. As far as we know, LGMA is the first attempt to perform Lie algebra transformation to project the original features in the Lie group space onto Lie algebra manifold space for domain adaptation. Comprehensive experiments validate that our approach considerably outperforms competitive methods on real-world datasets.