  The Semi-Algebraic framework for the approximate Canonical Polyadic (CP)
decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient
tool for the computation of the CP decomposition. The SECSI framework
reformulates the CP decomposition into a set of joint eigenvalue decomposition
(JEVD) problems. Solving all JEVDs, we obtain multiple estimates of the factor
matrices and the best estimate is chosen in a subsequent step by using an
exhaustive search or some heuristic strategy that reduces the computational
complexity. Moreover, the SECSI framework retains the option of choosing the
number of JEVDs to be solved, thus providing an adjustable complexity-accuracy
trade-off. In this work, we provide an analytical performance analysis of the
SECSI framework for the computation of the approximate CP decomposition of a
noise corrupted low-rank tensor, where we derive closed-form expressions of the
relative mean square error for each of the estimated factor matrices. These
expressions are obtained using a first-order perturbation analysis and 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.
Simulation results exhibit an excellent match between the obtained closed-form
expressions and the empirical results. Moreover, we propose a new Performance
Analysis based Selection (PAS) scheme to choose the final factor matrix
estimate. The results show that the proposed PAS scheme outperforms the
existing heuristics, especially in the high SNR regime.
