Tensor Chain Decomposition and Function Interpolation

0574036 - ÚTIA 2024 RIV US eng C - Conference Paper (international conference)
Tichavský, Petr - Phan, A. H.
Tensor Chain Decomposition and Function Interpolation.
Proceedings of the 22nd IEEE Statistical Signal Processing Workshop. Piscataway: IEEE, 2023, s. 557-561. ISBN 978-1-6654-5244-1.
[IEEE Statistical Signal Processing Workshop /22./. Hanoi (VN), 02.07.2023-05.07.2023]
R&D Projects: GA ČR(CZ) GA22-11101S
Institutional support: RVO:67985556
Keywords : multilinear models * tensor train * Rosenbrock function
OECD category: Electrical and electronic engineering
http://library.utia.cas.cz/separaty/2023/SI/tichavsky-0574036.pdf

Tensor Chain (TC) decomposition represents a given tensor as a chain (circle) of order-3 tensors (wagons) connected through tensor contractions. In this paper, we show the link between the TC decomposition and a structured Tucker decompositions, and propose a variant of the Krylov-Levenberg-Marquardt optimization, tailored for this problem. Many extensions can be considered, here we only mention decomposition of tensor with missing entries, which enables the tensor completion. Performance of the proposed algorithm is demonstrated on tensor decomposition of the sampled Rosenbrock function. It can be better modeled both as TC and canonical polyadic (CP) decomposition, but with TC, the reconstruction is possible with a lower number of function values.
Permanent Link: https://hdl.handle.net/11104/0344729