A review of quadratic discriminant analysis for high‐dimensional data

Quadratic discriminant analysis (QDA) is a classical and flexible classification approach, which allows differences between groups not only due to mean vectors but also covariance matrices. Modern high‐dimensional data bring us opportunities and also challenges. In the framework of classical QDA, the inverse of each sample covariance matrix is essential, but high‐dimensionality causes singularity in sample covariance matrices. To overcome this technical difficulty, several high‐dimensional QDA approaches with desirable theoretical properties emerge in recent years. We are to discuss the challenges, some existing works, and possibly several future directions with regard to high‐dimensional QDA. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification