Static and incremental robust kernel factorization embedding graph regularization supporting ill-conditioned industrial data recovery

Low-rank approximation algorithms aim to utilize convex nuclear norm constraint of linear matrices to recover ill-conditioned entries caused by multi-sampling rates, sensor drop-out. However, these existing algorithms are often limited in solving high-dimensionality and rank minimization relaxation. In this paper, a robust kernel factorization embedding graph regularization method is developed to statically impute missing measurements. Specifically, the implicit high-dimensional feature space of ill-conditioned data is factorized by kernel sparse dictionary. Then, a robust sparse-norm and graph regularization constraints are performed in the objective function to ensure the consistency of the spatial information. For the optimization of the parameters involved in the model, a distributed adaptive proximal Newton gradient descent learning strategy is proposed to accelerate the convergence. Furthermore, considering the dynamic time-series and potentially non-stationary structure of industrial data, we propose extended incremental versions to alleviate the complexity of the overall model computation. Extensive data recovery experiments are conducted on two real industrial processes to evaluate the proposed method in comparison with existing state-of-the-art restorers. The results show that the proposed methods can impute better with different missing rates and have strong competitiveness in practical application.