{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:58Z","timestamp":1753880878968,"version":"3.41.2"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"National Key Research and Development Program of China","award":["2020YFA0714200"],"award-info":[{"award-number":["2020YFA0714200"]}]},{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["61772011"],"award-info":[{"award-number":["61772011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Intelligent Information Processing Key Laboratory of Shanxi Province","award":["CICIP2018002"],"award-info":[{"award-number":["CICIP2018002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p> The generalization is one of the main concerns of machine learning method. k-SVCR is an important multi-class classification algorithm, but there is no theoretical analysis on the generalization of k-SVCR algorithm up to now. Therefore, in this paper, we consider multi-class support vector classification and regression (MSVCR) algorithm. We first establish the generalization bounds of MSVCR based on uniformly ergodic Markovian chain (u.e.M.c.) samples, and obtain its fast learning rate of MSVCR. As applications, we estimate the generalization of MSVCR for independent and identically distributed (i.i.d.) observations and strongly mixing observations, respectively. We also propose a new MSVCR algorithm based on q-times Markovian resampling (MSVCR-Mar-q). The experimental studies indicate that compared to the classical k-SVCR and other multi-class SVM algorithms, the proposed algorithm not only has smaller misclassification rate, but also has less sampling and training total time. <\/jats:p>","DOI":"10.1142\/s0219691322500175","type":"journal-article","created":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T16:28:58Z","timestamp":1652372938000},"source":"Crossref","is-referenced-by-count":1,"title":["Generalization and learning rate of multi-class support vector classification and regression"],"prefix":"10.1142","volume":"20","author":[{"given":"Zijie","family":"Dong","sequence":"first","affiliation":[{"name":"School of Mathematics and Economics, Hubei University of Education, Second Gaoxin Road, Wuhan 430205, Hubei, China"}]},{"given":"Jiawen","family":"Gong","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, 430062 Wuhan, P. R. 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