Computation of Regularized Linear Discriminant Analysis

Authors: Jan Kalina, Zdeněk Valenta, Jurjen Duintjer Tebbens
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of COMPSTAT 2014
Projects: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications
Bibliographic citation: KALINA, Jan, VALENTA, Zdeněk, DUINTJER TEBBENS, Jurjen. Computation of Regularized Linear Discriminant Analysis. In: GILLI, M., NIETO-REYES, A., GONZÁLEZ-RODRÍGUEZ, G., eds. Proceedings of COMPSTAT 2014. Geneva: Centre International de Conferences, 2014, S. 1-8. ISBN 978-2-8399-1347-8.
ID: 431042

Abstract

This paper is focused on regularized versions of classification analysis and their computation for high-dimensional data. A variety of regularized classification methods has been proposed and we critically discuss their computational aspects. We formulate several new algorithms for shrinkage linear discriminant analysis, which exploits a shrinkage covariance matrix estimator towards a regular target matrix. Numerical linear algebra considerations are used to propose tailor-made algorithms for specific choices of the target matrix. Further, we arrive at proposing a new classification method based on L2-regularization of group means and the pooled covariance matrix and accompany it by an efficient algorithm for its computation.