Dynamic and static Lagrange multiplier μ based Bayesian CP factorization with orthogonal factors: Theory and applications

The existing $\mu$-Singular Value Decomposition ($\mu$-SVD) denoising algorithm is capable of extracting gear fault information under strong noise conditions. However, this algorithm is only applicable to two-dimensional real-valued data and lacks a mechanism for implementing Automatic Rank Determination (ARD) in high-dimensional data. In this paper, a Bayesian and Tensor treatment of $\mu$-SVD is employed to enable ARD. To further investigate the impact of the Lagrange multiplier $\mu$ on the proposed $\mu$-variational Bayesian ($\mu$-VB) algorithm, we examine its performance from both static and dynamic perspectives. Simulation results demonstrate that the $\mu$-VB algorithm achieves ARD and performs well in noise reduction. Further the $\mu$-VB algorithm performs better in wireless communication and linear image coding across numerical domains, tensor sizes, orthogonal factors, and $\mu$ settings.