Regularized Periodic Gaussian Process for Nonparametric Sparse Feature Extraction From Noisy Periodic Signals

This study proposes a nonparametric sparse feature extraction approach based on a periodic Gaussian process (PGP) for highly nonlinear sparse periodic signals, which may not be effectively modeled by conventional linear models based on user-specified dictionaries. The PGP model is reformulated as a mixed-effects model. Hence a regularization term is allowed to be imposed on the random effect of the PGP model, called regularized PGP (RPGP) in this study, for sparse feature extraction. Unlike conventional sparse models, the proposed RPGP can simultaneously model fixed and random effects (global trend and local sparsity) of the signals. A computationally scalable algorithm based on the alternating direction method of multipliers (ADMM) is tailored for RPGP to iteratively optimize the fixed and random effects. The efficient computation of RPGP is achieved by a customized circulant-based acceleration technique that utilizes fast Fourier transform on circulant matrices. The performance of RPGP is evaluated through a simulation study on synthetic signals and a case study on real vibration signals.