Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method

Abstract

Classification using linear discriminant analysis (LDA) is challenging when the number of variables is large relative to the number of observations. Algorithms such as LDA require the computation of the feature vector’s precision matrices. In a high-dimension setting, due to the singularity of the covariance matrix, it is not possible to estimate the maximum likelihood estimator of the precision matrix. In this paper, we employ the Stein-type shrinkage estimation of Ledoit and Wolf for high-dimensional data classification. The proposed approach’s efficiency is numerically compared to existing methods, including LDA, cross-validation, gLasso, and SVM. We use the misclassification error criterion for comparison.

Keywords

• classification
• linear discriminant analysis
• high-dimensional data
• Ledoit and Wolf shrinkage method
• Stein-type shrinkage
• misclassification error