Multiclass Sparse Discriminant Analysis

摘要

In recent years many sparse linear discriminant analysis methods have beenproposed for high-dimensional classification and variable selection. However,most of these proposals focus on binary classification and they are notdirectly applicable to multiclass classification problems. There are two sparsediscriminant analysis methods that can handle multiclass classificationproblems, but their theoretical justifications remain unknown. In this paper,we propose a new multiclass sparse discriminant analysis method that estimatesall discriminant directions simultaneously. We show that when applied to thebinary case our proposal yields a classification direction that is equivalentto those by two successful binary sparse LDA methods in the literature. Anefficient algorithm is developed for computing our method with high-dimensionaldata. Variable selection consistency and rates of convergence are establishedunder the ultrahigh dimensionality setting. We further demonstrate the superiorperformance of our proposal over the existing methods on simulated and realdata.