caa a22 4500 467939268 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7207-1 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7207-1 The consistency of multicategory support vector machines [Elektronische Daten] [Di-Rong Chen, Dao-Hong Xiang] The goal of classification (or pattern recognition) is to construct a classifier with small misclassification error. The notions of consistency and universal consistency are important to the construction of classification rules. A consistent rule guarantees us that taking more samples essentially suffices to roughly reconstruct the unknown distribution. Support vector machine (SVM) algorithm is one of the most important rules in two category classification. How to effectively extend the SVM for multicategory classification is still an on-going research issue. Different versions of multicategory support vector machines (MSVMs) have been proposed and used in practice. We study the one designed by Lee, Lin and Wahba with hinge loss functional. The consistency of MSVMs is established under a mild condition. As a corollary, the universal consistency holds true if the reproducing kernel Hilbert space is dense in C norm. In addition, an example is given to demonstrate the main results. Springer, 2006 classification nationallicence consistency nationallicence universal consistency nationallicence misclassification error nationallicence support vector machine nationallicence Bayes rule nationallicence reproducing kernel Hilbert space nationallicence Chen Di-Rong Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, 100083, Beijing, P. R. China aut Xiang Dao-Hong Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, 100083, Beijing, P. R. China aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 155-169 1019-7168 24:1-4<155 2006 24 10444 https://doi.org/10.1007/s10444-004-7207-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7207-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Di-Rong Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, 100083, Beijing, P. R. China aut NATIONALLICENCE 700 1- Xiang Dao-Hong Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, 100083, Beijing, P. R. China aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 155-169 1019-7168 24:1-4<155 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer