Laplacian regularized robust principal component analysis for process monitoring. (August 2020) - Xiu, Xianchao; Yang, Ying; Kong, Lingchen; Liu, Wanquan
Abstract: Principal component analysis (PCA) is one of the most widely used techniques for process monitoring. However, it is highly sensitive to sparse errors because of the assumption that data only contains an underlying low-rank structure. To improve classical PCA in this regard, a novel Laplacian regularized robust principal component analysis (LRPCA) framework is proposed, where the "robust" comes from the introduction of a sparse term. By taking advantage of the hypergraph Laplacian, LRPCA not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information. An efficient alternating direction method of multipliers is designed with convergence guarantee. The resulting subproblems either have closed-form solutions or can be solved by fast solvers. Numerical experiments, including a simulation example and the Tennessee Eastman process, are conducted to illustrate the improved process monitoring performance of the proposed LRPCA. Highlights: To the best of author's knowledge, we are the first to model PCA in such a sparse and hypergraph Laplacian regularized framework. An efficient alternating direction method of multipliers (ADMM) with convergence analysis is developed to optimize LRPCA. Experiments on a simulation example and the TE practical process are conducted to illustrate the superiority of our proposed method.