A review of quadratic discriminant analysis for high‐dimensional data. (17th May 2018)

• Record Type: Journal Article
• Authors: Qin, Yingli
• Is Part Of: Wiley interdisciplinary reviews. Volume 10:Number 4(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-05-17
• Subjects: classification -- covariance matrix -- high‐dimensional -- misclassification probability -- quadratic discriminant analysis; Mathematical statistics -- Data processing -- Periodicals; Science -- Data processing -- Periodicals; Social sciences -- Data processing -- Periodicals; Mathematical statistics -- Periodicals; 519.50285
• DOI: 10.1002/wics.1434
• Languages: English
• ISSNs: 1939-5108

Abstract

Abstract : 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 Abstract : High‐dimensional QDA.