First-Order Perturbation Analysis of Secsi With Generalized Unfoldings

Abstract

Tensor decompositions are regarded as a powerful tool for multidimensional signal processing. In this contribution, we focus on the well-known Canonical Polyadic (CP) decomposition and present a first-order perturbation analysis of the SEmi-algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalization with Generalized Unfoldings (SECSI-GU), which is advantageous for tensors of an order higher than three. Numerical results indicate that the analytical relative Mean Square Factor Error (rMSFE) of the estimated factor matrices resulting from each generalized unfolding considered in SECSI -GU matches the empirical rMSFE very well. As SECSI -GU considers all possible partitionings of the tensor modes resulting in a large number of candidate factor matrix estimates, an exhaustive search-based criterion to select the final factor matrix estimates leads to a prohibitive computational complexity. The accurate performance prediction achieved by the first-order perturbation analysis conducted in this paper will significantly facilitate the selection of the final factor matrix estimates in an efficient manner and will therefore contribute to a low-complexity enhancement of SECSI-GU.