—We propose a novel reconstruction based transfer learning method called Latent Sparse Domain Transfer (LSDT) for domain adaptation and visual categorization of heterogeneous data. For handling cross-domain distribution mismatch, we advocate reconstructing the target domain data with the combined source and target domain data points based on -norm sparse coding. Furthermore, we propose a joint learning model for simultaneous optimization of the sparse coding and the optimal subspace representation. Additionally, we generalize the proposed LSDT model into a kernel based linear/nonlinear basis transformation learning framework for tackling nonlinear subspace shifts in Reproduced Kernel Hilbert Space. The proposed methods have three advantages: 1) the latent space and reconstruction are jointly learned for pursuit of an optimal subspace transfer; 2) with the theory of sparse subspace clustering (SSC), a few valuable source and target data points are formulated to reconstruct the target ...