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Feature selection in SVM via polyhedral k-norm

Manlio Gaudioso (manlio.gaudioso***at***unical.it)
Enrico Gorgone (egorgone***at***unica.it)
Jean-Baptiste Hiriart-Urruty (jbhu***at***math.univ-toulouse.fr)

Abstract: We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo--norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate between $\|.\|_1$ and $\|.\|_{\infty}$, plays a significant role, allowing us to come out with a DC (Difference of Convex) optimization problem that is tackled by means of DCA algorithm. The results of several numerical experiments on benchmark classification datasets are reported.

Keywords: Sparse optimization, Cardinality constraint, k-norm, Support Vector Machine, DC optimization

Category 1: Global Optimization

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation: Optimization Letters, to appear

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Entry Submitted: 11/11/2018
Entry Accepted: 11/12/2018
Entry Last Modified: 09/10/2019

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