Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification

The SVM classifier often uses radial basis kernel because it has just one tunable hyperparameter, unlike polynomial kernel that has three. However, the polynomial kernel is separable and may speed up the SVM training and test, although with high degrees it is still slow because it requires many mono...

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Detalles Bibliográficos
Autores: Fernández Delgado, Manuel, Pereira-Costa, A. L., Cernadas García, Eva
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:dnet:minerva_____::0931fb22cc3a790994be6a369e2f395a
Acceso en línea:https://hdl.handle.net/10347/47589
Access Level:acceso abierto
Palabra clave:Support vector machine
Classification
Quadratic kernel
Hyperparameter tuning
3304 Tecnología de los ordenadores
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oai_identifier_str oai:dnet:minerva_____::0931fb22cc3a790994be6a369e2f395a
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spelling Linear complexity hyperparameter tuning of the quadratic kernel for support vector classificationFernández Delgado, ManuelPereira-Costa, A. L.Cernadas García, EvaSupport vector machineClassificationQuadratic kernelHyperparameter tuning3304 Tecnología de los ordenadoresThe SVM classifier often uses radial basis kernel because it has just one tunable hyperparameter, unlike polynomial kernel that has three. However, the polynomial kernel is separable and may speed up the SVM training and test, although with high degrees it is still slow because it requires many monomials. On the contrary, low degree (e.g. quadratic) polynomial kernels keep the number of monomials low even with high-dimensional inputs, being faster and extending the applicability of SVM to large scale datasets. We prove experimentally that quadratic polynomial kernel with just one hyperparameter achieves performance similar to radial basis kernel. We propose a method named increasing quadratic estimation, IQE, that calculates the hyperparameter value using only the training data, without SVM training. The proposed IQE achieves state-of-the-art performance and is very fast, because its complexity is linear on the training set size and dimensionality. The experimental work, performed on a collection of 120 classification datasets, proves that IQE: 1) outperforms and is faster than quadratic kernel without tuning; 2) is similar to radial basis and quadratic kernels tuned using grid search, being one or two orders of magnitude faster; and 3) outperforms genetic, Bayesian and particle swarm optimization, being between three and five orders of magnitude faster. Code is available from https://osf.io/nz96q Open Science Framework (OSF).ElsevierUniversidade de Santiago de Compostela. Departamento de Electrónica e ComputaciónUniversidade de Santiago de Compostela. Centro de Investigación en Tecnoloxías Intelixentes da USC (CiTIUS)20262026-01-0120262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/47589reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2© 2026 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:dnet:minerva_____::0931fb22cc3a790994be6a369e2f395a2026-06-15T12:47:27Z
dc.title.none.fl_str_mv Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
title Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
spellingShingle Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
Fernández Delgado, Manuel
Support vector machine
Classification
Quadratic kernel
Hyperparameter tuning
3304 Tecnología de los ordenadores
title_short Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
title_full Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
title_fullStr Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
title_full_unstemmed Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
title_sort Linear complexity hyperparameter tuning of the quadratic kernel for support vector classification
dc.creator.none.fl_str_mv Fernández Delgado, Manuel
Pereira-Costa, A. L.
Cernadas García, Eva
author Fernández Delgado, Manuel
author_facet Fernández Delgado, Manuel
Pereira-Costa, A. L.
Cernadas García, Eva
author_role author
author2 Pereira-Costa, A. L.
Cernadas García, Eva
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Electrónica e Computación
Universidade de Santiago de Compostela. Centro de Investigación en Tecnoloxías Intelixentes da USC (CiTIUS)
dc.subject.none.fl_str_mv Support vector machine
Classification
Quadratic kernel
Hyperparameter tuning
3304 Tecnología de los ordenadores
topic Support vector machine
Classification
Quadratic kernel
Hyperparameter tuning
3304 Tecnología de los ordenadores
description The SVM classifier often uses radial basis kernel because it has just one tunable hyperparameter, unlike polynomial kernel that has three. However, the polynomial kernel is separable and may speed up the SVM training and test, although with high degrees it is still slow because it requires many monomials. On the contrary, low degree (e.g. quadratic) polynomial kernels keep the number of monomials low even with high-dimensional inputs, being faster and extending the applicability of SVM to large scale datasets. We prove experimentally that quadratic polynomial kernel with just one hyperparameter achieves performance similar to radial basis kernel. We propose a method named increasing quadratic estimation, IQE, that calculates the hyperparameter value using only the training data, without SVM training. The proposed IQE achieves state-of-the-art performance and is very fast, because its complexity is linear on the training set size and dimensionality. The experimental work, performed on a collection of 120 classification datasets, proves that IQE: 1) outperforms and is faster than quadratic kernel without tuning; 2) is similar to radial basis and quadratic kernels tuned using grid search, being one or two orders of magnitude faster; and 3) outperforms genetic, Bayesian and particle swarm optimization, being between three and five orders of magnitude faster. Code is available from https://osf.io/nz96q Open Science Framework (OSF).
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/47589
url https://hdl.handle.net/10347/47589
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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