New Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition
(2022) SIAM Journal on Matrix Analysis and Applications — Vol. 43, n° 2, p. 840-866 (2022)
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- Abstract
- We propose new Riemannian preconditioned algorithms for low-rank tensor comple-tion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric onthe product space of the factor matrices of the low-rank tensor in the polyadic decomposition form.This new metric is designed using an approximation of the diagonal blocks of the Hessian of thetensor completion cost function and thus has a preconditioning effect on these algorithms. We provethat the proposed Riemannian gradient descent algorithm globally converges to a stationary pointof the tensor completion problem, with convergence rate estimates using the \Lojasiewicz property.Numerical results on synthetic and real-world data suggest that the proposed algorithms are moreefficient in memory and time compared to state-of-the-art algorithms. Moreover, the proposed algo-rithms display a greater tolerance for overestimated rank parameters in terms of the tensor recoveryperformance and thus enable a flexible choice of the rank parameter.
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Citations
Dong, S., Gao, B., Guan, Y., & Glineur, F. (2022). New Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition. SIAM Journal on Matrix Analysis and Applications, 43(2), 840-866. https://doi.org/10.1137/21M1394734 (Original work published 2022)