Performance analysis of least-squares khatri-rao factorization

The least-squares Khatri-Rao factorization is regarded as an important linear- and multilinear-algebraic tool and finds applications in, for instance, computation of the CP decomposition and channel estimation for two-way relaying systems. We conduct a “first-order” perturbation analysis for it, which is a crucial step towards establishing analytical performance evaluation of various schemes employing the least-squares Khatri-Rao factorization. Numerical results validating our analytical performance analysis are shown. Being new advance in perturbation analysis on matrix decompositions, the performance analysis of the least-squares Khatri-Rao factorization presented in this paper will also contribute to a promising enhancement of the SECSI-GU framework, which is able to estimate the loading matrices in a CP decomposition, both efficiently and accurately.