{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T10:02:15Z","timestamp":1764842535735,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This research was funded by the NSRF, and NU, Thailand","award":["R2564B024."],"award-info":[{"award-number":["R2564B024."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.<\/jats:p>","DOI":"10.3390\/sym13091652","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T21:28:45Z","timestamp":1631136525000},"page":"1652","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Stochastic Subgradient for Large-Scale Support Vector Machine Using the Generalized Pinball Loss Function"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9367-5204","authenticated-orcid":false,"given":"Wanida","family":"Panup","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5715-3804","authenticated-orcid":false,"given":"Rabian","family":"Wangkeeree","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"},{"name":"Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vapnik, V.N. 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