Change search
ReferencesLink to record
Permanent link

Direct link
Fixed points, fractals, iterated function systems and generalized support vector machines
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0865-7248
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 [en]
support vector machine, fixed points, iterated function system, variational inequality
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33511ISBN: 978-91-7485-302-5OAI: oai:DiVA.org:mdh-33511DiVA: diva2:1045320
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
List of papers
1. Fractals of Generalized F-Hutchinson Operator in b-Metric Spaces
Open this publication in new window or tab >>Fractals of Generalized F-Hutchinson Operator in b-Metric Spaces
2016 (English)In: Journal of Operators, ISSN 2314-5064, Vol. 2016, 9 pp- p., 5250394Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature.

Place, publisher, year, edition, pages
Hindawi Publishing Corporation, 2016
Keyword
fractals, attractor, iterated function system, F-contraction, b-metric space
National Category
Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33093 (URN)10.1155/2016/5250394 (DOI)
Projects
FUSION
Available from: 2016-09-08 Created: 2016-09-07 Last updated: 2016-12-05Bibliographically approved
2. Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines
Open this publication in new window or tab >>Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines
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
support vector machine, generalized support vector machine, control function
National Category
Computational Mathematics Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33094 (URN)10.1007/978-3-319-42105-6 (DOI)978-3-319-42104-9 (ISBN)978-3-319-42105-6 (ISBN)
Projects
FUSION
Available from: 2016-09-08 Created: 2016-09-07 Last updated: 2016-12-05Bibliographically approved
3. Linear and Nonlinear Classifiers of Data withSupport Vector Machines and GeneralizedSupport Vector Machines
Open this publication in new window or tab >>Linear and Nonlinear Classifiers of Data withSupport Vector Machines and GeneralizedSupport Vector Machines
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]

The support vector machine for linear and nonlinear classification of datais studied. The notion of generalized support vector machine for data classifications is used. The problem of generalized support vector machine is shown to be equivalent to the problem of generalized variational inequality and various results for the existence of solutions are established. Moreover, examples supporting the results are provided.

Place, publisher, year, edition, pages
Springer, 2016
Series
, Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 179
Keyword
generalized support vector machine, data classification, generalized variational inequality
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33385 (URN)10.1007/978-3-319-42105-6 (DOI)978-3-319-42104-9 (ISBN)978-3-319-42105-6 (ISBN)
Available from: 2016-10-11 Created: 2016-10-11 Last updated: 2016-12-05Bibliographically approved
4. Data classification with support vector machine and generalized support vector machine
Open this publication in new window or tab >>Data classification with support vector machine and generalized support vector machine
2016 (English)Conference paper, Abstract (Refereed)
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.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:mdh:diva-33508 (URN)
Conference
International Conference on Nonlinear Problems in Aviation and Aerospace, July 05-08, 2016
Available from: 2016-11-08 Created: 2016-11-08 Last updated: 2016-11-09

Open Access in DiVA

fulltext(402 kB)19 downloads
File information
File name FULLTEXT01.pdfFile size 402 kBChecksum SHA-512
92c49fc54c1a46fe4a20120f0dc279958b7fce0cb5191e6de110be4446cd6e1bf92443071770d9d72eb7d0aa742d45044b291b283d9c1b8d629237dbd60d0650
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Qi, Xiaomin
By organisation
Educational Sciences and Mathematics
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 19 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 94 hits
ReferencesLink to record
Permanent link

Direct link