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.

中文翻译：

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用于过程监控的拉普拉斯正则化稳健主成分分析

摘要 主成分分析 (PCA) 是最广泛使用的过程监控技术之一。然而，它对稀疏错误高度敏感，因为假设数据只包含一个底层的低秩结构。为了在这方面改进经典 PCA，提出了一种新颖的拉普拉斯正则化稳健主成分分析 (LRPCA) 框架，其中“稳健”来自引入稀疏项。通过利用超图拉普拉斯算子，LRPCA 不仅可以表示全局低维结构，还可以捕获内在的非线性几何信息。设计了一种有效的乘法器交替方向方法，并保证收敛。由此产生的子问题要么具有封闭形式的解决方案，要么可以通过快速求解器解决。数值实验，