Graph-Regularized Orthogonal Non-Negative Matrix Factorization with Itakura–Saito (IS) Divergence for Fault Detection

Yabing Liu, Juncheng Wu (), Jin Zhang and Man-Fai Leung
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Yabing Liu: College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
Juncheng Wu: School of Mechanical Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
Jin Zhang: School of Computing and Information Science, Faculty of Science and Engineering, Anglia Ruskin University, Cambridge CB1 1PT, UK
Man-Fai Leung: School of Computing and Information Science, Faculty of Science and Engineering, Anglia Ruskin University, Cambridge CB1 1PT, UK

Mathematics, 2025, vol. 13, issue 15, 1-18

Abstract: In modern industrial environments, quickly and accurately identifying faults is crucial for ensuring the smooth operation of production processes. Non-negative Matrix Factorization (NMF)-based fault detection technology has garnered attention due to its wide application in industrial process monitoring and machinery fault diagnosis. As an effective dimensionality reduction tool, NMF can decompose complex datasets into non-negative matrices with practical and physical significance, thereby extracting key features of the process. This paper presents a novel approach to fault detection in industrial processes, called Graph-Regularized Orthogonal Non-negative Matrix Factorization with Itakura–Saito Divergence (GONMF-IS). The proposed method addresses the challenges of fault detection in complex, non-Gaussian industrial environments. By using Itakura–Saito divergence, GONMF-IS effectively handles data with probabilistic distribution characteristics, improving the model’s ability to process non-Gaussian data. Additionally, graph regularization leverages the structural relationships among data points to refine the matrix factorization process, enhancing the robustness and adaptability of the algorithm. The incorporation of orthogonality constraints further enhances the independence and interpretability of the resulting factors. Through extensive experiments, the GONMF-IS method demonstrates superior performance in fault detection tasks, providing an effective and reliable tool for industrial applications. The results suggest that GONMF-IS offers significant improvements over traditional methods, offering a more robust and accurate solution for fault diagnosis in complex industrial settings.

Keywords: fault detection; non-negative matrix factorization; Itakura-Saito divergence; non-Gaussian process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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