research-article

Kernel projection algorithm for large-scale SVM problems

Authors:

Jiaqi Wang,

Qing Tao,

Jue WangAuthors Info & Claims

Journal of Computer Science and Technology, Volume 17, Issue 5

Pages 556 - 564

https://doi.org/10.1007/BF02948824

Published: 01 August 2002 Publication History

Abstract

Support Vector Machine (SVM) has become a very effective method in statistical machine learning and it has proved that training SMV is to solve Nearest Point pair Problem (NPP) between two disjoint closed convex sets. Later Keerthi pointed out that it is difficult to apply classical excellent geometric algorithms direcly to SVM and so designed a new geometric algorithm for SVM. In this article, a new algorithm for geometrically solving SVM, Kernel Projection Algorithm, is presented based on the theorem on fixed-points of projection mapping. This new algorithm makes it easy to apply classical geometric algorithms to solving SVM and is more understandable than Keerthi’s. Experiments show that the new algorithm can also handle large-scale SVM problems. Geometric algorithms for SVM, such as Keerthi’s algorithm, require that two closed convex sets be disjoint and otherwise the algorithms are meaningless. In this article, this requirement will be guaranteed in theory by using the theoretic result on universal kernel functions.

References

[1]

Vapnik V. Statistical Learning Theory. Addison-Wiley, 1998.

Google Scholar

[2]

Bennett R and Bredensteiner E J Geometry in Learning 1996 New York Department of Mathematical Sciences, Rennselaer Polytechnic Institutes

Google Scholar

[3]

Keerthi S S, Shevade S K, Bhattacharyya C, et al. A fast iterative nearest point algorithm for support vector machine classifier desing IEE Transactions on Neural Networks 2000 11 1 124-136

Crossref

Google Scholar

[4]

Crisp D J and Burges C J C A geometric interpretation of μ-SVM classifiers NIPS 2000 12 244-250

Google Scholar

[5]

Tao Qing, Sun Dermin, Fan Jinsong. The maximal margin linear classifier based on the contraction of the closed convex hull. To appear inJournal of Software.

Google Scholar

[6]

Llanas B and de Sevilla M F An interative algorithm for finding a nearest pair of points in two convex subsets ofRⁿ Computers and Mathematics with Applications 2000 40 971-983

Crossref

Google Scholar

[7]

Platt J Scholkopf B, Burges C J C, and Smola A J Fast training of support vector machines using sequential minimal optimization Advances in Kernel Methods—Support Vector Learning 1999 Cambridge, MA MIT Press 185-208

Google Scholar

[8]

Gilbert E G Minimizing the quadratic form on a convex set SIAM J. Contr. 1966 4 61-79

Crossref

Google Scholar

[9]

Mitchell B F, Dem’yanov V F, and Malozemov V N Finding the point of a polyhedron closest to the origin SIAM J. Contr. 1974 12 19-26

Crossref

Google Scholar

[10]

Gilbert E G, Johnson D W, and Keerthi S S A fast procedure computing the distance between complex objects in three dimension space IEEE J. Robot. Automat. 1988 4 193-203

Crossref

Google Scholar

[11]

Muller K R et al. An introduction to kernel-based learning algorithms IEEE Trans. Neural Networks 2001 12 2 181-201

Crossref

Google Scholar

[12]

Tao Qing, Wu Gaowei, Wang Jue. The theoretical analysis of kernel technique and kernel covering approach. Technique Report, Institute of Automation, Chinese Academy of Sciences, 2001.

Google Scholar

[13]

Tao Qing, Wang Jiaqi, Wang Jue. Soft kernel projection algorithm for support vector machines. Technique Report, Institute of Automation, Chinese Academy of Sciences, 2001.

Google Scholar

Cited By

View all

Wang DFang W(2006)GPCA method for fraud detection in mobile communication networksProceedings of the 5th WSEAS international conference on Telecommunications and informatics10.5555/1974762.1974777(76-79)Online publication date: 27-May-2006
https://dl.acm.org/doi/10.5555/1974762.1974777
Wang JWu XZhang C(2005)Support vector machines based on K-means clustering for real-time business intelligence systemsInternational Journal of Business Intelligence and Data Mining10.1504/IJBIDM.2005.0073181:1(54-64)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1504/IJBIDM.2005.007318
Tao QWu GWang J(2004)A generalized S-K algorithm for learning v-SVM classifiersPattern Recognition Letters10.1016/j.patrec.2004.03.01125:10(1165-1171)Online publication date: 16-Jul-2004
https://dl.acm.org/doi/10.1016/j.patrec.2004.03.011

Index Terms

Kernel projection algorithm for large-scale SVM problems

Index terms have been assigned to the content through auto-classification.

Recommendations

Projection Support Vector Machine Generators

Large-scale Support Vector Machine (SVM) classification is a very active research line in data mining. In recent years, several efficient SVM generation algorithms based on quadratic problems have been proposed, including: Successive OverRelaxation (SOR)...
Fast SVM classifier for large-scale classification problems
Abstract
Support vector machines (SVM), as one of effective and popular classification tools, have been widely applied in various fields. However, they may incur prohibitive computational costs when solving large-scale classification problems. ...
Highlights
- The new SVM model. We construct a new SVM model, which is named as truncated squared hinge loss SVM model.
An Efficient Support Vector Machine Algorithm for Solving Multi-class Pattern Recognition Problems
ICCMS '10: Proceedings of the 2010 Second International Conference on Computer Modeling and Simulation - Volume 02

In this paper, an efficient support vector machine (SVM) algorithm for solving multi-class pattern recognition problems is proposed. The samples in each class are trained by one-class SVM (OCSVM), respectively. And then several sets of support vectors (...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Journal of Computer Science and Technology

Journal of Computer Science and Technology Volume 17, Issue 5

Sep 2002

144 pages

ISSN:1000-9000

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 2002

Revision received: 28 May 2002

Received: 28 December 2001

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 22 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Wang DFang W(2006)GPCA method for fraud detection in mobile communication networksProceedings of the 5th WSEAS international conference on Telecommunications and informatics10.5555/1974762.1974777(76-79)Online publication date: 27-May-2006
https://dl.acm.org/doi/10.5555/1974762.1974777
Wang JWu XZhang C(2005)Support vector machines based on K-means clustering for real-time business intelligence systemsInternational Journal of Business Intelligence and Data Mining10.1504/IJBIDM.2005.0073181:1(54-64)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1504/IJBIDM.2005.007318
Tao QWu GWang J(2004)A generalized S-K algorithm for learning v-SVM classifiersPattern Recognition Letters10.1016/j.patrec.2004.03.01125:10(1165-1171)Online publication date: 16-Jul-2004
https://dl.acm.org/doi/10.1016/j.patrec.2004.03.011

View Options

View options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Projection Support Vector Machine Generators

Fast SVM classifier for large-scale classification problems

An Efficient Support Vector Machine Algorithm for Solving Multi-class Pattern Recognition Problems

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations