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arXiv · 1410.6131

Penalized versus constrained generalized eigenvalue problems

Irina Gaynanova·James Booth·Martin T. Wells
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Abstract

We investigate the difference between using an $\ell_1$ penalty versus an $\ell_1$ constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an $\ell_1$ penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an $\ell_1$ constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of an $\ell_1$ constraint in the context of discriminant analysis and principal component analysis.

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Irina Gaynanova, James Booth, Martin T. Wells. 2014-10-22. Penalized versus constrained generalized eigenvalue problems. https://doi.org/10.1080/10618600.2016.1172017

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