Proximal Alternating Linearized Minimization Algorithm for Sparse Tensor Train Decomposition (Statistics, Optimization & Information Computing, 2025)
We address the sparse tensor train (TT) decomposition problem by incorporating an L1-norm regularization term. To improve numerical stability, orthogonality constraints are imposed on the problem. The tensor is expressed in the TT format, and the proximal alternating linearized minimization (PALM) algorithm is employed to solve the problem. Furthermore, we verify that the objective function qualifies as a Kurdyka-Lojasiewicz (KL) function and provide a convergence analysis. Numerical experiments on synthetic data and real data also demonstrate the efficiency of the proposed algorithm.