A Comprehensive Review on Discriminant Analysis for Addressing Challenges of Class-Level Limitations, Small Sample Size, and Robustness

The classical linear discriminant analysis (LDA) algorithm has three primary drawbacks, i.e., small sample size problem, sensitivity to noise and outliers, and inability to deal with multi-modal-class data. This paper reviews LDA technology and its variants, covering the taxonomy and characteristics of these technologies and comparing their innovations and developments in addressing these three shortcomings. Additionally, we describe the application areas and emphasize the kernel extensions of these technologies to solve nonlinear problems. Most importantly, this paper presents perspectives on future research directions and potential research areas in this field.