Hossein Moosaei and Milan Hladík. Bounds for sparse solutions of K-SVCR multi-class classification model. In Dimitris E. Simos et al., editor, Learning and Intelligent Optimization, LNCS, pp. 136–144, Springer, Cham, 2022.
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The support vector classification-regression machine for k-class classification (K-SVCR) is a novel multi-class classification approach based on the 1-versus-1-versus-rest structure. In this work, we suggested an efficient model by proposing the p-norm (0 < p < 1) instead of the 2-norm for the regularization term in the objective function of K-SVCR that can be used for feature selection. We derived lower bounds for the absolute value of nonzero entries in every local optimal solution of the p-norm based model. Also, we provided upper bounds for the number of nonzero components of the optimal solutions. We explored the link between solution sparsity, regularization parameters, and the p-choice.
@inCollection{MooHla2022b,
author = "Hossein Moosaei and Milan Hlad\'{\i}k",
title = "Bounds for sparse solutions of {K-SVCR} multi-class classification model",
editor = "Simos et al., Dimitris E.",
feditor = "Simos, Dimitris E. and Rasskazova, Varvara A. and Archetti, Francesco and Kotsireas, Ilias S. and Pardalos, Panos M.",
booktitle = "Learning and Intelligent Optimization",
fbooktitle = "Learning and Intelligent Optimization, 16th International Conference, LION 16
Milos Island, Greece, June 5-10, 2022, Revised Selected Papers",
publisher = "Springer",
address = "Cham",
series = "LNCS",
fseries = "Lecture Notes in Computer Science",
volume = "13621",
pages = "136-144",
year = "2022",
doi = "10.1007/978-3-031-24866-5_11",
isbn = "978-3-031-24866-5",
issn = "0302-9743",
url = "https://doi.org/10.1007/978-3-031-24866-5_11",
bib2html_dl_html = "https://link.springer.com/chapter/10.1007/978-3-031-24866-5_11",
bib2html_dl_pdf = "https://rdcu.be/c5uVt",
abstract = "The support vector classification-regression machine for k-class classification (K-SVCR) is a novel multi-class classification approach based on the 1-versus-1-versus-rest structure. In this work, we suggested an efficient model by proposing the p-norm (0 < p < 1) instead of the 2-norm for the regularization term in the objective function of K-SVCR that can be used for feature selection. We derived lower bounds for the absolute value of nonzero entries in every local optimal solution of the p-norm based model. Also, we provided upper bounds for the number of nonzero components of the optimal solutions. We explored the link between solution sparsity, regularization parameters, and the p-choice.",
keywords = "K-SVCR; Multi-class classification; First-order optimally condition; Sparsity; p-norm",
}
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