Structured Low-Rank Tensor Learning
This work addresses tensor learning with structural constraints, which is incremental as it builds on existing low-rank tensor methods by introducing a new factorization and optimization approach.
The paper tackles the problem of learning low-rank tensors from partial observations with structural constraints by proposing a novel factorization that simplifies optimization, and it develops Riemannian optimization algorithms with experimental verification on constraints like nonnegative and Hankel.
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an optimization problem on manifolds. We develop first-order and second-order Riemannian optimization algorithms to solve it. The duality gap for the resulting problem is derived, and we experimentally verify the correctness of the proposed algorithm. We demonstrate the algorithm on nonnegative constraints and Hankel constraints.