The sparse and low-rank interpretation of SVD-based denoising for vibration signals

Abstract

Vibration signal denoising is one of the most important steps in condition monitoring and fault diagnosis, and SVD-based methods are a vital part of advanced signal denoising due to their non-parametric and simple properties. The relationships between SVD-based denoising and other advanced signal processing methods are very significant and can help speed up the development of SVD-based denoising methods. There is limited prior work into the sparse and low-rank meaning of SVD-based denoising. In this paper, we build the relationships among SVDbased denoising, sparse l0-norm minimization, sparse weighted l1-norm minimization, and weighted low-rank model, when the dictionary is designed by left and right singular matrices in sparse minimization. Using the derived conclusion, we establish weighted soft singular value decomposition (WSSVD) for vibration signal denoising. Finally, we perform one experimental study to verify the effectiveness of WSSVD considering impulse interference and amplitude fidelity.Index Terms-Sparse and low-rank, SVD-based denoising, vibration signal processing

Drug–target interaction prediction using unifying of graph regularized nuclear norm with bilinear factorization

“…The purpose of the LRMF concerning the input matrix Y is to factorize it to the product of two low rank matrices that can be used to reconstruct the low rank matrix X with exceptional fidelity. A variety of LRMF-based methods, such as classical Singular Value Decomposition (SVD) under ' L 2 − norm ' [50,51], robust LRMF methods under ' L 1 − norm ' [52,53] and other probabilistic methods have been proposed [54,55]. The problem of Low rank models for recovering a rank-k matrix Z can be expressed by minimizing Eq.…”