Penalized versus constrained generalized eigenvalue problems
Irina Gaynanova, James Booth, Martin T. Wells(Submitted on 22 Oct 2014 (v1), last revised 23 Oct 2014 (this version, v2))
We investigate the difference between using an ℓ1 penalty versus an ℓ1 constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an ℓ1 penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an ℓ1 constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of an ℓ1 constraint in the context of discriminant analysis.
Comments: 13 pages, 4 figuresSubjects: Computation (stat.CO); Machine Learning (stat.ML)Cite as: arXiv:1410.6131 [stat.CO] (or arXiv:1410.6131v2 [stat.CO] for this version)