Penalized Versus Constrained Generalized Eigenvalue Problems Academic Article

abstract

• 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. We investigate the difference between using an 1 penalty versus an 1 constraint in generalized eigenvalue problems arising in multivariate analysis. Our main finding is that the 1 penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an 1 constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of the 1 constraint in the context of discriminant analysis and principal component analysis. Supplementary materials for this article are available online.

authors

• Gaynanova, Irina

published proceedings

• JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS

author list (cited authors)

• Gaynanova, I., Booth, J. G., & Wells, M. T.

citation count

• 7

complete list of authors

• Gaynanova, Irina||Booth, James G||Wells, Martin T

publication date

• April 2017

publisher

• Taylor & Francis  Publisher

published in

• Journal of Computational and Graphical Statistics  Journal

keywords

• Discriminant Analysis
• Duality Gap
• Nonconvex Optimization
• Variable Selection

Digital Object Identifier (DOI)

• 10.1080/10618600.2016.1172017

start page

• 379

end page

• 387

volume

• 26

issue

• 2