Riemannian preconditioned coordinate descent for low multi-linear rank approximation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914721661190144 |
|---|---|
| author | Hamed, Mohammad Hosseini, Reshad |
| author_facet | Hamed, Mohammad Hosseini, Reshad |
| contents | This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold. We use a Riemmanian coordinate descent method for solving the problem, and also provide a global convergence analysis matching that of the coordinate descent method in the Euclidean setting. We also show that each step of our method with the unit step-size is actually a step of the orthogonal iteration algorithm. Experimental results show the computational advantage of our method for high-dimensional tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01632 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Riemannian preconditioned coordinate descent for low multi-linear rank approximation Hamed, Mohammad Hosseini, Reshad Optimization and Control 15A69, 58D17, 90C26 This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold. We use a Riemmanian coordinate descent method for solving the problem, and also provide a global convergence analysis matching that of the coordinate descent method in the Euclidean setting. We also show that each step of our method with the unit step-size is actually a step of the orthogonal iteration algorithm. Experimental results show the computational advantage of our method for high-dimensional tensors. |
| title | Riemannian preconditioned coordinate descent for low multi-linear rank approximation |
| topic | Optimization and Control 15A69, 58D17, 90C26 |
| url | https://arxiv.org/abs/2109.01632 |