Fault diagnosis by Locality Preserving Discriminant Analysis and its kernel variation

Abstract

Linear Discriminant Analysis (LDA) and its nonlinear kernel variation Generalized Discriminant Analysis (GDA) are the most popular supervised dimensionality reduction methods for fault diagnosis. However, we argue that they probably provide suboptimal results for fault diagnosis due to the Fisher's criterion they use. This paper proposes a new supervised dimensionality reduction method named Locality Preserving Discriminant Analysis (LPDA) and its kernel variation Kernel LPDA (KLPDA) for fault diagnosis. (K)LPDA maximizes a new criterion such that local discriminant structure and local geometric structure in data are optimally preserved simultaneously in each dimension of the reduced space. The criterion directly targets at minimizing local overlapping between different classes. Extensive simulations on the Tennessee Eastman (TE) benchmark simulation process and a waste water treatment plant (WWTP) clearly demonstrate the superiority of our methods in terms of misclassification rate and making use of extra training data.