Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method
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 c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/4069 |
| _version_ | 1797467395577610240 |
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| author | Rasoul Lotfi Davood Shahsavani Mohammad Arashi |
| author_facet | Rasoul Lotfi Davood Shahsavani Mohammad Arashi |
| author_sort | Rasoul Lotfi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T18:52:02Z |
| format | Article |
| id | doaj.art-92fdf170794b450aa9d19f7b59c45830 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:52:02Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-92fdf170794b450aa9d19f7b59c458302023-11-24T05:44:25ZengMDPI AGMathematics2227-73902022-11-011021406910.3390/math10214069Classification in High Dimension Using the Ledoit–Wolf Shrinkage MethodRasoul Lotfi0Davood Shahsavani1Mohammad Arashi2Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, IranDepartment of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, IranDepartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, IranClassification 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.https://www.mdpi.com/2227-7390/10/21/4069classificationlinear discriminant analysishigh-dimensional dataLedoit and Wolf shrinkage methodStein-type shrinkagemisclassification error |
| spellingShingle | Rasoul Lotfi Davood Shahsavani Mohammad Arashi Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method Mathematics classification linear discriminant analysis high-dimensional data Ledoit and Wolf shrinkage method Stein-type shrinkage misclassification error |
| title | Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method |
| title_full | Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method |
| title_fullStr | Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method |
| title_full_unstemmed | Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method |
| title_short | Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method |
| title_sort | classification in high dimension using the ledoit wolf shrinkage method |
| topic | classification linear discriminant analysis high-dimensional data Ledoit and Wolf shrinkage method Stein-type shrinkage misclassification error |
| url | https://www.mdpi.com/2227-7390/10/21/4069 |
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