# Bibliography

Journal Article

### Non-orthogonal tensor diagonalization

, ,

**: **Signal Processing vol.138, 1 (2017), p. 313-320

**: **GA14-13713S, GA ČR,
GA17-00902S, GA ČR

**: **multilinear models,
canonical polyadic decomposition,
parallel factor analysis

**: **10.1016/j.sigpro.2017.04.001

**: **http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0474387.pdf

**(eng): **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\nthe 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\ndiagonalization 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\ndiagonalization 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\ntraditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithm\ncan either outperform the existing block-term decomposition algorithms, or produce good initial points for their application.

**: **BB

**: **10103