General Graph Regularized Semi-Nonnegative Matrix Factorization and its application for industrial process monitoring

The nonnegative matrix factorization (NMF)-based fault detection methods have achieved significant success, but they still face several challenges in practical applications. Existing approaches mainly focus on generating spatially localized, sparse, and part-based subspace representations, but often overlook biases in data distribution, which negatively affects monitoring performance. To address this issue, this article proposes a general graph regularized semi-NMF (GGSNMF) method for statistical process monitoring. This method is capable of extracting common features between samples in a lower-dimensional space while preserving the special features of the data. Additionally, by incorporating manifold regularization, it maintains the local geometric structure of the data. By integrating the latent variables extracted by GGSNMF with process monitoring techniques, the method is successfully applied to fault detection. Experimental results on benchmark datasets demonstrate that the proposed method exhibits superior performance in fault detection.