Feature selection in SVM via polyhedral k-norm

Manlio Gaudioso (1) , E Gorgone (2) , Jean-Baptiste Hiriart-Urruty (3)

1 Unical - Università della Calabria [Arcavacata di Rende]
2 UniCa - Università degli Studi di Cagliari = University of Cagliari
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the L-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 k-norm , intermediate between L-1 and L-∞ norms, 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.

Mots clés: Sparse optimization; Cardinality constraint; k-norm; Support Vector Machine; DC optimization

Domaines: Mathématiques [math]; Informatique [cs]; Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Manlio Gaudioso, E Gorgone, Jean-Baptiste Hiriart-Urruty. Feature selection in SVM via polyhedral k-norm. Optimization Letters, 2020, 14, pp.19-36. ⟨10.1007/s11590-019-01482-1⟩. ⟨hal-01977766⟩