A Convengent Solution to Tensor Subspace Learning

Recently, substantial efforts have been devoted to the subspace learning techniques based on tensor representation, such as 2DLDA [Ye et al., 2004], DATER [Yan et al., 2005] and Tensor Subspace Analysis (TSA) [He et al., 2005]. In this context, a vital yet unsolved problem is that the computational convergency of these iterative algorithms is not guaranteed. In this work, we present a novel solution procedure for general tensor-based subspace learning, followed by a detailed convergency proof of the solution projection matrices and the objective function value. Extensive experiments on real-world databases verify the high convergence speed of the proposed procedure, as well as its superiority in classification capability over traditional solution procedures.