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Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology. (MAM)ORCID iD: 0000-0001-6516-3212
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0865-7248
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2016 (English)In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)
Abstract [en]

In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We showthat 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. Moreover, we provide various examples to support our results.

Place, publisher, year, edition, pages
Springer, 2016.
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 179
Keyword [en]
support vector machine, generalized support vector machine, control function
National Category
Computational Mathematics Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33094DOI: 10.1007/978-3-319-42105-6ISBN: 978-3-319-42104-9 (print)ISBN: 978-3-319-42105-6 (print)OAI: oai:DiVA.org:mdh-33094DiVA: diva2:963086
Projects
FUSION
Available from: 2016-09-08 Created: 2016-09-07 Last updated: 2016-12-05Bibliographically approved
In thesis
1. Fixed points, fractals, iterated function systems and generalized support vector machines
Open this publication in new window or tab >>Fixed points, fractals, iterated function systems and generalized support vector machines
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Västerås: Mälardalen University Press, 2016. 66 p.
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 247
Keyword
support vector machine, fixed points, iterated function system, variational inequality
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33511 (URN)978-91-7485-302-5 (ISBN)
Presentation
2016-12-12, U2-016, Mälardalen University, Västerås, 14:15 (English)
Opponent
Supervisors
Projects
FUSION
Available from: 2016-11-09 Created: 2016-11-08 Last updated: 2016-11-24Bibliographically approved

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CiteExportLink to record
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Citation style
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