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Data classification with support vector machine and generalized support vector machine
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0002-0865-7248
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
Department of Mathematics, COMSATS Institute of Information Technology.ORCID-id: 0000-0001-6516-3212
2017 (engelsk)Inngår i: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, 2017, Vol. 1798, s. 020126-1-020126-9, artikkel-id 020126Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

In the paper, we study the theory of support vector machine and the using for linear and nonlinear classification of data. And we also used the notion of generalized support vector machine for data classifications. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions.

sted, utgiver, år, opplag, sider
2017. Vol. 1798, s. 020126-1-020126-9, artikkel-id 020126
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-33508DOI: 10.1063/1.4972718ISI: 000399203000125Scopus ID: 2-s2.0-85013642228ISBN: 9780735414648 (tryckt)OAI: oai:DiVA.org:mdh-33508DiVA, id: diva2:1045285
Konferanse
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016; University of La RochelleLa Rochelle; France; 4 July 2016 through 8 July 2016
Tilgjengelig fra: 2016-11-08 Laget: 2016-11-08 Sist oppdatert: 2017-09-03bibliografisk kontrollert
Inngår i avhandling
1. Fixed points, fractals, iterated function systems and generalized support vector machines
Åpne denne publikasjonen i ny fane eller vindu >>Fixed points, fractals, iterated function systems and generalized support vector machines
2016 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established.

sted, utgiver, år, opplag, sider
Västerås: Mälardalen University Press, 2016. s. 66
Serie
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 247
Emneord
support vector machine, fixed points, iterated function system, variational inequality
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-33511 (URN)978-91-7485-302-5 (ISBN)
Presentation
2016-12-12, U2-016, Mälardalen University, Västerås, 14:15 (engelsk)
Opponent
Veileder
Prosjekter
FUSION
Tilgjengelig fra: 2016-11-09 Laget: 2016-11-08 Sist oppdatert: 2016-11-24bibliografisk kontrollert

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