ADHERENTLY PENALIZED LINEAR DISCRIMINANT ANALYSIS

Abstract

A problem of supervised learning in which the data consist of p features and n observations is considered. Each observation is assumed to belong to either one of the two classes. Linear discriminant analysis (LDA) has been widely used for both classification and dimensionality reduction in this setting. However, when the dimensionality p is high and the observations are scarce, LDA does not offer a satisfactory result for classification. Witten & Tibshirani (2011) proposed the penalized LDA based on the Fisher’s discriminant problem with sparsity penalization. In this paper, an elastic-net type penalization is considered for LDA, and the corresponding optimization problem is efficiently solved.