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Article: A C-Eigenvalue Problem for Tensors with Applications to Higher-order Multivariate Markov Chains

TitleA C-Eigenvalue Problem for Tensors with Applications to Higher-order Multivariate Markov Chains
Authors
KeywordsEigenpair
Tensor
Higher-order
Multivariate
Markov chain
Stationary probability distribution
Issue Date2019
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa
Citation
Computers & Mathematics with Applications, 2019, v. 78 n. 3, p. 1008-1025 How to Cite?
AbstractIn this paper, we study a new tensor eigenvalue problem, which involves - and -eigenvalues as its special cases. Some theoretical results such as existence of an eigenvalue and the number of eigenvalues are given. For an application of the proposed eigenvalue problem, we establish a tensor model for a higher-order multivariate Markov chain. The core issue of this problem is to study a stationary probability distribution of a higher-order multivariate Markov chain. A sufficient condition of the unique stationary positive distribution is given. An algorithm for computing stationary probability distribution is also developed. Numerical examples of applications in stock market modeling, sales demand prediction and biological sequence analysis are given to illustrate the proposed tensor model and the computed stationary probability distribution can provide a better prediction in these Markov chain applications.
Persistent Identifierhttp://hdl.handle.net/10722/275050
ISSN
2017 Impact Factor: 1.86
2015 SCImago Journal Rankings: 1.092
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, W-
dc.contributor.authorKe, R-
dc.contributor.authorChing, WK-
dc.contributor.authorNg, KP-
dc.date.accessioned2019-09-10T02:34:25Z-
dc.date.available2019-09-10T02:34:25Z-
dc.date.issued2019-
dc.identifier.citationComputers & Mathematics with Applications, 2019, v. 78 n. 3, p. 1008-1025-
dc.identifier.issn0898-1221-
dc.identifier.urihttp://hdl.handle.net/10722/275050-
dc.description.abstractIn this paper, we study a new tensor eigenvalue problem, which involves - and -eigenvalues as its special cases. Some theoretical results such as existence of an eigenvalue and the number of eigenvalues are given. For an application of the proposed eigenvalue problem, we establish a tensor model for a higher-order multivariate Markov chain. The core issue of this problem is to study a stationary probability distribution of a higher-order multivariate Markov chain. A sufficient condition of the unique stationary positive distribution is given. An algorithm for computing stationary probability distribution is also developed. Numerical examples of applications in stock market modeling, sales demand prediction and biological sequence analysis are given to illustrate the proposed tensor model and the computed stationary probability distribution can provide a better prediction in these Markov chain applications.-
dc.languageeng-
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa-
dc.relation.ispartofComputers & Mathematics with Applications-
dc.subjectEigenpair-
dc.subjectTensor-
dc.subjectHigher-order-
dc.subjectMultivariate-
dc.subjectMarkov chain-
dc.subjectStationary probability distribution-
dc.titleA C-Eigenvalue Problem for Tensors with Applications to Higher-order Multivariate Markov Chains-
dc.typeArticle-
dc.identifier.emailChing, WK: wching@hku.hk-
dc.identifier.emailNg, KP: kkpong@hku.hk-
dc.identifier.authorityChing, WK=rp00679-
dc.identifier.authorityNg, KP=rp02578-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.camwa.2019.03.016-
dc.identifier.scopuseid_2-s2.0-85063494932-
dc.identifier.hkuros303658-
dc.identifier.volume78-
dc.identifier.issue3-
dc.identifier.spage1008-
dc.identifier.epage1025-
dc.identifier.isiWOS:000473376400020-
dc.publisher.placeUnited Kingdom-

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