NDLI: SVM Training: Second-Order Cone Programming versus Quadratic Programming

Content Provider	IEEE Xplore Digital Library
Author	Debnath, R. Takahashi, H.
Copyright Year	2006
Description	Author affiliation: Computer Science and Engineering Discipline, Khulna University, Khulna-9208, Bangladesh. e-mail: ramesward@gmail.com (Debnath, R.)
Abstract	The support vector machine (SVM) problem is a convex quadratic programming problem which scales with the training data size. If the training size is large, the problem cannot be solved by straighforward methods. The large-scale SVM problems are tackled by applying chunking (decomposition) technique. The quadratic programming problem involves a square matrix which is called kernel matrix is positive semi-definite. That is, the rank of the kernel matrix is less than or equal to its size. In this paper we discuss a method that can exploit the low-rank of the kernel matrix, and an interior-point method (IPM) is efficiently applied to the global (large-sized) problem. The method is based on the technique of second-order cone programming (SOCP). This method reformulates the SVM's quadratic programming problem into the second-order cone programming problem. The SOCP method is much faster than efficient softwares $SVM^{light}and$ SVMTorch if the rank of the kernel matrix is small enough compared to the training set size or if the kernel matrix can be approximated by a low-rank positive semidefinite matrix.
Starting Page	1162
Ending Page	1168
File Size	322629
Page Count	7
File Format	PDF
ISBN	0780394909
DOI	10.1109/IJCNN.2006.246822
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-16
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quadratic programming Support vector machines Kernel Training data Matrix decomposition Support vector machine classification Large-scale systems Computational complexity Optimization methods Machine learning
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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