Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI)

The Canonical Polyadic (CP) decomposition of R-way arrays is a powerful tool in multi-dimensional signal processing. There exists many methods to compute the CP decomposition. In particular, the Semi-Algebraic framework for the approximate Canonical Polyadic (CP) decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient and flexible framework for the computation of the CP decomposition. In this work, we perform a first-order performance analysis of the SECSI framework for the computation of the approximate CP decomposition of a noise corrupted low-rank 3-way tensor. We provide closed-form expressions of the relative Mean Square Factor Error (rMSFE) for each of the estimated factor matrices. The derived expressions are formulated in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. The numerical results depict the excellent match between the closed-form expressions and the empirical results.