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Article: Incremental CP Tensor Decomposition by Alternating Minimization Method

TitleIncremental CP Tensor Decomposition by Alternating Minimization Method
Authors
KeywordsAlternating minimization
CP decomposition
Incremental tensor
Issue Date2021
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php
Citation
SIAM Journal on Matrix Analysis and Applications, 2021, v. 42 n. 2, p. 832-858 How to Cite?
AbstractIn practical applications, incremental tensors are very common: only a portion of tensor data is available, and new data are arriving in the next time step or continuously over time. To handle this type of tensors time-saving algorithms are required for online computation. In this paper, we consider incremental CP (CANDECOMP/PARAFAC) decomposition, which requires one to update the CP decomposition after new tensor data, together with the exiting tensor, are ready for analysis. There exist several incremental CP decomposition algorithms, but almost all of these algorithms assume that the number of CP decomposition components remains fixed in the incremental process. The main contribution of this paper is the study of how to add components in the incremental CP decomposition. We derive the coordinate representation of the incremental CP decomposition with respect to a special basis and show related properties of tensor rank and the uniqueness of such incremental CP decomposition. Under the framework of this representation, the proposed method can be solved by using an alternating minimization algorithm. Numerical examples are presented to show the good performance of the proposed algorithms in terms of computational time and data fitting compared with existing methods.
Persistent Identifierhttp://hdl.handle.net/10722/304241
ISSN
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 1.042
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZeng, C-
dc.contributor.authorNg, KP-
dc.date.accessioned2021-09-23T08:57:14Z-
dc.date.available2021-09-23T08:57:14Z-
dc.date.issued2021-
dc.identifier.citationSIAM Journal on Matrix Analysis and Applications, 2021, v. 42 n. 2, p. 832-858-
dc.identifier.issn0895-4798-
dc.identifier.urihttp://hdl.handle.net/10722/304241-
dc.description.abstractIn practical applications, incremental tensors are very common: only a portion of tensor data is available, and new data are arriving in the next time step or continuously over time. To handle this type of tensors time-saving algorithms are required for online computation. In this paper, we consider incremental CP (CANDECOMP/PARAFAC) decomposition, which requires one to update the CP decomposition after new tensor data, together with the exiting tensor, are ready for analysis. There exist several incremental CP decomposition algorithms, but almost all of these algorithms assume that the number of CP decomposition components remains fixed in the incremental process. The main contribution of this paper is the study of how to add components in the incremental CP decomposition. We derive the coordinate representation of the incremental CP decomposition with respect to a special basis and show related properties of tensor rank and the uniqueness of such incremental CP decomposition. Under the framework of this representation, the proposed method can be solved by using an alternating minimization algorithm. Numerical examples are presented to show the good performance of the proposed algorithms in terms of computational time and data fitting compared with existing methods.-
dc.languageeng-
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php-
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applications-
dc.rights© [year] Society for Industrial and Applied Mathematics. First Published in [Publication] in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM).-
dc.subjectAlternating minimization-
dc.subjectCP decomposition-
dc.subjectIncremental tensor-
dc.titleIncremental CP Tensor Decomposition by Alternating Minimization Method-
dc.typeArticle-
dc.identifier.emailZeng, C: zengchao@nankai.edu.cn-
dc.identifier.emailNg, KP: michael.ng@hku.hk-
dc.identifier.authorityNg, KP=rp02578-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/20M1319097-
dc.identifier.hkuros325161-
dc.identifier.volume42-
dc.identifier.issue2-
dc.identifier.spage832-
dc.identifier.epage858-
dc.identifier.isiWOS:000674142000017-
dc.publisher.placeUnited States-

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