| Theoretical analysis for solution of support vector data description. | |
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MedLine Citation:
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PMID: 21353975 Owner: NLM Status: In-Data-Review |
Abstract/OtherAbstract:
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As we may know well, uniqueness of the Support Vector Machines (SVM) solution has been solved. However, whether Support Vector Data Description (SVDD), another best-known machine learning method, has a unique solution or not still remains unsolved. Due to the fact that the primal optimization of SVDD is not a convex programming problem, it is difficult for us to theoretically analyze the SVDD solution in an analogous way to SVM. In this paper, we concentrate on the theoretical analysis for the solution to the primal optimization problem of SVDD. We first reformulate equivalently the primal optimization problem of SVDD into a convex programming problem, and then prove that the optimal solution with respect to the sphere center is unique, derive the necessary and sufficient conditions of non-uniqueness of the optimal solution with respect to the sphere radius in the primal optimization problem of SVDD. Moreover, we also explore the property of the SVDD solution from the perspective of the SVDD dual form. Furthermore, according to the geometric interpretation of SVDD, a method of computing the sphere radius is proposed when the optimal solution with respect to the sphere radius in the primal optimization problem is non-unique. Finally, we have several examples to illustrate these findings. |
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Authors:
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Xiaoming Wang; Fu-Lai Chung; Shitong Wang |
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Publication Detail:
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Type: Journal Article Date: 2011-02-03 |
Journal Detail:
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Title: Neural networks : the official journal of the International Neural Network Society Volume: 24 ISSN: 1879-2782 ISO Abbreviation: Neural Netw Publication Date: 2011 May |
Date Detail:
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Created Date: 2011-02-28 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 8805018 Medline TA: Neural Netw Country: United States |
Other Details:
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Languages: eng Pagination: 360-9 Citation Subset: IM |
Copyright Information:
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Copyright © 2011 Elsevier Ltd. All rights reserved. |
Affiliation:
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School of Information, Jiangnan University, Wuxi, Jiangsu, China; Department of Computing, HongKong Polytechnic University, Hong Kong, China. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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