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Article: Solving sparse non-negative tensor equations: algorithms and applications
Title | Solving sparse non-negative tensor equations: algorithms and applications |
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Authors | |
Keywords | information retrieval multivariate polynomial equation iterative method multi-dimensional network Nonnegative tensor community |
Issue Date | 2015 |
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 Identifier | http://hdl.handle.net/10722/276694 |
ISSN | 2023 Impact Factor: 0.8 2020 SCImago Journal Rankings: 0.482 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, Xutao | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:23Z | - |
dc.date.available | 2019-09-18T08:34:23Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Frontiers of Mathematics in China, 2015, v. 10, n. 3, p. 649-680 | - |
dc.identifier.issn | 1673-3452 | - |
dc.identifier.uri | http://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.language | eng | - |
dc.relation.ispartof | Frontiers of Mathematics in China | - |
dc.subject | information retrieval | - |
dc.subject | multivariate polynomial equation | - |
dc.subject | iterative method | - |
dc.subject | multi-dimensional network | - |
dc.subject | Nonnegative tensor | - |
dc.subject | community | - |
dc.title | Solving sparse non-negative tensor equations: algorithms and applications | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11464-014-0377-3 | - |
dc.identifier.scopus | eid_2-s2.0-84939897948 | - |
dc.identifier.volume | 10 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 649 | - |
dc.identifier.epage | 680 | - |
dc.identifier.eissn | 1673-3576 | - |
dc.identifier.isi | WOS:000355622500010 | - |
dc.identifier.issnl | 1673-3452 | - |