Penalized Versus Constrained Generalized Eigenvalue Problems Academic Article uri icon


  • 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.

published proceedings


altmetric score

  • 1

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