Lagrangian relaxation for SVM feature selection

•Feature selection for SVM is stated as a Mixed Binary Linear Programming problem.•Lagrangian relaxation and dual ascent are applied to the model.•Both a lower and an upper bound available at each iteration.•Numerical results on benchmark datasets are given. We discuss a Lagrangian-relaxation-based...

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Veröffentlicht in:Computers & operations research Jg. 87; S. 137 - 145
Hauptverfasser: Gaudioso, M., Gorgone, E., Labbé, M., Rodríguez-Chía, A.M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Ltd 01.11.2017
Pergamon Press Inc
Elsevier
Schlagworte:
Algorithms
Ascent
Computer Science
Consolidation
Feature selection
Heuristic
Lagrangian relaxation
Linear programming
Nonsmooth optimization
Operations Research
Optimization
Studies
Support vector machines
SVM classification
SVM classification
Feature selection
Nonsmooth optimization
Lagrangian relaxation
feature selection
nonsmooth optimiza- tion
ISSN:0305-0548, 1873-765X, 0305-0548
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Zusammenfassung:•Feature selection for SVM is stated as a Mixed Binary Linear Programming problem.•Lagrangian relaxation and dual ascent are applied to the model.•Both a lower and an upper bound available at each iteration.•Numerical results on benchmark datasets are given. 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.
Bibliographie:ObjectType-Article-1
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2017.06.001