Name
Title | ||
|---|---|---|
New Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition |
Abstract | ||
|---|---|---|
We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the 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 the tensor completion cost function, thus has a preconditioning effect on these algorithms. We prove that the proposed Riemannian gradient descent algorithm globally converges to a stationary point of the tensor completion problem, with convergence rate estimates using the $\L{}$ojasiewicz property. Numerical results on synthetic and real-world data suggest that the proposed algorithms are more efficient in memory and time compared to state-of-the-art algorithms. Moreover, the proposed algorithms display a greater tolerance for overestimated rank parameters in terms of the tensor recovery performance, thus enable a flexible choice of the rank parameter. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1137/21M1394734 | SIAM J. Matrix Anal. Appl. |
DocType | Volume | Citations |
Journal | 43 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuyu Dong | 1 | 0 | 1.01 |
| Bin Gao | 2 | 61 | 3.80 |
| Yu Guan | 3 | 27 | 5.06 |
| François Glineur | 4 | 3 | 1.09 |