Non-orthogonal tensor diagonalization

0474387 - ÚTIA 2018 RIV NL eng J - Journal Article
Tichavský, Petr - Phan, A. H. - Cichocki, A.
Non-orthogonal tensor diagonalization.
Signal Processing. Roč. 138, č. 1 (2017), s. 313-320. ISSN 0165-1684. E-ISSN 1872-7557
R&D Projects: GA ČR(CZ) GA14-13713S; GA ČR GA17-00902S
Institutional support: RVO:67985556
Keywords : multilinear models * canonical polyadic decomposition * parallel factor analysis
OECD category: Statistics and probability
Impact factor: 3.470, year: 2017
http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0474387.pdf

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of
the tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetric
diagonalization of an order-three tensor, (2) a similar algorithm for a non-symmetric AJD, also called a two-sided diagonalization of an order-three tensor, and (3) an algorithm for three-sided
diagonalization of order-three or order-four tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and in certain scenarios they can outperform
traditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithm
can either outperform the existing block-term decomposition algorithms, or produce good initial points for their application.
Permanent Link: http://hdl.handle.net/11104/0271454