title: Covariance-enhanced discriminant analysis.
abstract: Linear discriminant analysis has been widely used to characterize or separate multiple classes via linear combinations of features. However, the high dimensionality of features from modern biological experiments defies traditional discriminant analysis techniques. Possible interfeature correlations present additional challenges and are often underused in modelling. In this paper, by incorporating possible interfeature correlations, we propose a covariance-enhanced discriminant analysis method that simultaneously and consistently selects informative features and identifies the corresponding discriminable classes. Under mild regularity conditions, we show that the method can achieve consistent parameter estimation and model selection, and can attain an asymptotically optimal misclassification rate. Extensive simulations have verified the utility of the method, which we apply to a renal transplantation trial.
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 211189, China.
authors.forename: Peirong
authors.initials: P
authors.lastname: Xu
authors.affiliation: Department of Statistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
authors.forename: J I
authors.initials: JI
authors.lastname: Zhu
authors.affiliation: Department of Mathematics, Hong Kong Baptist University, Hong Kong, China.
authors.forename: Lixing
authors.initials: L
authors.lastname: Zhu
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
authors.forename: Y I
authors.initials: YI
authors.lastname: Li
keywords: Correlation; Graphical lasso; Linear discriminant analysis; Pairwise fusion; Variable selection