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User: yuji-sutou

Structured Low-Rank Tensor Learning. (arXiv:2305.07967v1 [cs.LG])

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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.

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