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Article: Solving sparse non-negative tensor equations: algorithms and applications

TitleSolving sparse non-negative tensor equations: algorithms and applications
Authors
Keywordsinformation retrieval
multivariate polynomial equation
iterative method
multi-dimensional network
Nonnegative tensor
community
Issue Date2015
Citation
Frontiers of Mathematics in China, 2015, v. 10, n. 3, p. 649-680 How to Cite?
Abstract© 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg. We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.
Persistent Identifierhttp://hdl.handle.net/10722/276694
ISSN
2017 Impact Factor: 0.377
2015 SCImago Journal Rankings: 0.362

 

DC FieldValueLanguage
dc.contributor.authorLi, Xutao-
dc.contributor.authorNg, Michael K.-
dc.date.accessioned2019-09-18T08:34:23Z-
dc.date.available2019-09-18T08:34:23Z-
dc.date.issued2015-
dc.identifier.citationFrontiers of Mathematics in China, 2015, v. 10, n. 3, p. 649-680-
dc.identifier.issn1673-3452-
dc.identifier.urihttp://hdl.handle.net/10722/276694-
dc.description.abstract© 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg. We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.-
dc.languageeng-
dc.relation.ispartofFrontiers of Mathematics in China-
dc.subjectinformation retrieval-
dc.subjectmultivariate polynomial equation-
dc.subjectiterative method-
dc.subjectmulti-dimensional network-
dc.subjectNonnegative tensor-
dc.subjectcommunity-
dc.titleSolving sparse non-negative tensor equations: algorithms and applications-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11464-014-0377-3-
dc.identifier.scopuseid_2-s2.0-84939897948-
dc.identifier.volume10-
dc.identifier.issue3-
dc.identifier.spage649-
dc.identifier.epage680-
dc.identifier.eissn1673-3576-

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