Sparse Robust Principal Component Analysis with Applications to Fault Detection and Diagnosis

Abstract

Principal component analysis (PCA) is a popular method for modeling and analysis of high-dimensional data. In spite of its advantages, classical PCA also has two drawbacks. First, it is very sensitive to outliers in the data. Second, it cannot yield interpretable PCs because most of the loadings are nonzero. To overcome these drawbacks, we propose a new PCA method that has the properties of robustness and sparsity at the same time, called sparse robust PCA (SRPCA). The robustness is achieved by taking a robust covariance matrix instead of the classical covariance matrix used in PCA. Meanwhile, an additional penalty is imposed on the number of nonzero loadings to achieve the sparsity. SRPCA is not only robust against outliers, but also can yield interpretable PCs. A robust process monitoring method is developed using SRPCA. A cumulative percent contribution criterion is proposed for selecting the optimal PCs for process monitoring. The selected PCs are used to define two fault detection indices. Based on t...