Name
Title | ||
|---|---|---|
Double coupled canonical polyadic decomposition of third-order tensors: Algebraic algorithm and relaxed uniqueness conditions |
Abstract | ||
|---|---|---|
Double coupled canonical polyadic decomposition (DC-CPD) decomposes multiple tensors with coupling in the first two modes, into minimal number of rank-1 tensors that also admit the double coupling structure. It has a particular interest in joint blind source separation (J-BSS) applications. In a preceding paper, we proposed an algebraic algorithm for underdetermined DC-CPD, of which the factor matrices in the first two modes of each tensor may have more columns than rows. It uses a pairwise coupled rank-1 detection mapping to transform a possibly underdetermined DC-CPD into an overdetermined DC-CPD, which can be solved algebraically via generalized eigenvalue decomposition (GEVD). In this paper, we generalize the pairwise or second-order coupled rank-1 detection mapping to an arbitrary order K≥2. Based on this generalized coupled rank-1 detection mapping, we propose a broad framework for the algebraic computation of DC-CPD, which consists of a series of algorithms with more relaxed working assumptions, each corresponding to a fixed order K≥2. Deterministic and generic uniqueness conditions are provided. We will show through analysis and numerical results that our new uniqueness conditions for DC-CPD are more relaxed than the existing results for DC-CPD and CPD. We will further show, through simulation results, the performance of the proposed algebraic DC-CPD framework in approximate DC-CPD and a J-BSS application, in comparison with existing DC-CPD and CPD algorithms. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.image.2018.10.006 | Signal Processing: Image Communication |
Keywords | Field | DocType |
Tensor,Canonical polyadic decomposition,Double coupled,Algebraic algorithm,Uniqueness | Uniqueness,Applied mathematics,Overdetermined system,Algebraic number,Underdetermined system,Tensor,Computer science,Matrix (mathematics),Symbolic computation,Theoretical computer science,Blind signal separation | Journal |
Volume | ISSN | Citations |
73 | 0923-5965 | 0 |
PageRank | References | Authors |
0.34 | 19 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiao-Feng Gong | 1 | 123 | 19.33 |
| Qiu-Hua Lin | 2 | 173 | 27.57 |
| Fengyu Cong | 3 | 151 | 24.72 |
| Lieven De Lathauwer | 4 | 3002 | 226.72 |