Linear discriminant analysis

Abstract

Linear discriminant analysis (LDA) is a versatile statistical method for reducing redundant and noisy information from an original sample to its essential features. Particularly, LDA is a supervised learning technique, in which the labelled data are necessary for its training process and have been widely used for data dimensionality reduction. Original data are transformed into a low-dimensional subspace by maximizing the trace of the between-class scatter matrix while minimizing the trace of the within-class scatter matrix, thereby enhancing the expressiveness of features. This Primer offers a thorough overview of LDA, including its definition and the interpretation of its numerical and graphical results. It details LDA variants, their implementation settings, experimental outcomes and widely used open-source databases. This Primer also explores applications of LDA-based methods, implementation details across various areas and connections with related methodologies. Reproducibility, limitation and optimization of LDA-based methods are discussed followed by future goals of LDA and its variants. Linear discriminant analysis (LDA) is a versatile statistical method for reducing redundant and noisy information from an original sample to its essential features. In this Primer, Zhao et al. discuss LDA variants and their implementation settings as well as best practices for applying LDA to analyse data.