Non-Convex Transfer Subspace Learning via Embedded Distribution Alignment

Transfer subspace learning plays a critical role in unsupervised domain adaptation by establishing a shared embedding space where source domain data can be linearly reconstructed to match target domain distribution. While existing methods exploit the low-rank structures of reconstruction matrix, they frequently overlook the alignment of cross-domain joint probability distributions in the learned low-dimensional subspace. To address these challenges, we propose a novel non-convex transfer learning method named DATSL, which employs embedded distribution alignment. Our DATSL incorporates a non-convex regularizer to approximate low-rank constraints, capturing the complex characteristics of the rank function by minimizing top $k$ smallest singular values of reconstruction matrix. To align the joint distributions across domains, a category-aware joint distribution alignment mechanism extracts more discriminative representations and enhances subspace discriminability through label-informed covariance matching. Besides, DATSL is extended to a graph-based variant GDATSL, which incorporates manifold-preserving constraints via Laplacian regularization to maintain intrinsic data topology during knowledge transfer. Furthermore, we develop an efficient iterative optimization algorithm to solve our formulated nonconvex minimization problems with proved convergence. Extensive experimental results on several public datasets demonstrate the effectiveness of our proposed methods in comparison to other state-of-the-art approaches.