We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in the Support Vector Machine (SVM) framework for binary classification. In particular we embed into our objective function a weighted combination of the L1 and L0 norm of the normal to the separating hyperplane. We come out with a Mixed Binary Linear Programming problem which is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we apply a consolidated nonsmooth optimization ascent algorithm to solve the resulting Lagrangian dual. In the proposed approach we get, at every ascent step, both a lower bound on the optimal solution as well as a feasible solution at low computational cost. We present the results of our numerical experiments on some benchmark datasets.

Lagrangian relaxation for SVM feature selection

GAUDIOSO, MANLIO;GORGONE, ENRICO;
2017-01-01

Abstract

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in the Support Vector Machine (SVM) framework for binary classification. In particular we embed into our objective function a weighted combination of the L1 and L0 norm of the normal to the separating hyperplane. We come out with a Mixed Binary Linear Programming problem which is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we apply a consolidated nonsmooth optimization ascent algorithm to solve the resulting Lagrangian dual. In the proposed approach we get, at every ascent step, both a lower bound on the optimal solution as well as a feasible solution at low computational cost. We present the results of our numerical experiments on some benchmark datasets.
2017
Feature selection; Lagrangian relaxation; Nonsmooth optimization; SVM classification; Computer science (all); Modeling and simulation; Management science and operations research
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/218765
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