Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method

• Published in: Mathematics (Basel) Vol. 10; no. 21; p. 4069
• Main Authors: Lotfi, Rasoul, Shahsavani, Davood, Arashi, Mohammad
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-11-2022
• Subjects: Algorithms; Analysis; Classification; Covariance matrix; Discriminant analysis; Factor analysis; Food science; high-dimensional data; Ledoit and Wolf shrinkage method; linear discriminant analysis; Matrices; Maximum likelihood estimates; Maximum likelihood estimates (Statistics); Maximum likelihood estimators; Methods; misclassification error; Normal distribution; Stein-type shrinkage; Iran
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10214069

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.