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A unitary joint diagonalization algorithm for nonsymmetric higher‐order tensors based on Givens‐like rotations
Author(s) -
Miao Jifei,
Cheng Guanghui,
Li Wenrui,
Moreau Eric
Publication year - 2020
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2291
Subject(s) - mathematics , unitary state , algorithm , orthogonal matrix , order (exchange) , tensor (intrinsic definition) , unitary transformation , joint (building) , rotation (mathematics) , set (abstract data type) , orthogonal basis , pure mathematics , geometry , computer science , architectural engineering , physics , finance , quantum mechanics , political science , law , economics , engineering , quantum , programming language
Summary Based on Givens‐like rotations, we present a unitary joint diagonalization algorithm for a set of nonsymmetric higher‐order tensors. Each unitary rotation matrix only depends on one unknown parameter which can be analytically obtained in an independent way following a reasonable assumption and a complex derivative technique. It can serve for the canonical polyadic decomposition of a higher‐order tensor with orthogonal factors. Furthermore, based on cross‐high‐order cumulants of observed signals, we show that the proposed algorithm can be applied to solve the joint blind source separation problem. The simulation results reveal that the proposed algorithm has a competitive performance compared with those of several existing related methods.