Name
Abstract | ||
|---|---|---|
A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We show that the LM algorithm has the same complexity of first-order optimisation algorithms, while the rotational method leads to solving the best rank-1 approximation of tensors of size $2 \times 2 \times \cdots \times 2$. We derive a closed-form expression of the best rank-1 tensor of $2\times 2 \times 2$ tensors and present an ALS algorithm which updates 3 component at a time for higher order tensors. The proposed algorithm is illustrated in decomposition of difficult tensors which are associated with multiplication of two matrices. |
Year | Venue | DocType |
|---|---|---|
2017 | CoRR | Journal |
Volume | Citations | PageRank |
abs/1709.08336 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anh Huy Phan | 1 | 828 | 51.60 |
| Petr Tichavský | 2 | 341 | 41.01 |
| Andrzej Cichocki | 3 | 5228 | 508.42 |