An Algebraic Coupled Canonical Polyadic Decomposition Algorithm via Joint Eigenvalue Decomposition

Abstract

Coupled canonical polyadic decomposition (C-CPD) has been widely applied in signal processing and data analysis. In this paper, we propose a new algebraic C-CPD algorithm based on joint eigenvalue decomposition (J-EVD). The proposed algorithm exploits the CPD structure of each tensor and the coupling among different tensors to construct a set of matrices that together admit a J-EVD, the algebraic computation of which yields the common factor matrix. Then, the remaining factor matrices can be obtained by rank-1 approximation with the obtained common factor matrix as prior knowledge. Numerical results are given to demonstrate the performance of the proposed algorithm in comparison with existing algebraic C-CPD algorithms.