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Soft Computing

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25.07.2020 | Focus

The use of grossone in elastic net regularization and sparse support vector machines

verfasst von: Renato De Leone, Nadaniela Egidi, Lorella Fatone

Erschienen in: Soft Computing | Ausgabe 23/2020

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Abstract

New algorithms for the numerical solution of optimization problems involving the \(l_{0}\) pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral \(\textcircled {1}\) (grossone) and indicating the number of elements of the set \({\text {I}}\!{\text {N}}\), of natural numbers. We show how the numerical system built upon \(\textcircled {1}\) and the proposed approximation of the \(l_0\) pseudo-norm in terms of \(\textcircled {1}\) can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems.

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Titel: The use of grossone in elastic net regularization and sparse support vector machines
verfasst von: Renato De Leone
Nadaniela Egidi
Lorella Fatone
Publikationsdatum: 25.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 23/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-05185-z

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