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Article: Total variation based tensor decomposition for multi-dimensional data with time dimension

TitleTotal variation based tensor decomposition for multi-dimensional data with time dimension
Authors
KeywordsAlternating direction method of multipliers
Regularization
Tensor decomposition
Time dimension
Total variation
Multidimensional data
Issue Date2015
Citation
Numerical Linear Algebra with Applications, 2015, v. 22, n. 6, p. 999-1019 How to Cite?
Abstract© 2015 John Wiley & Sons, Ltd. In this paper, we study tensors with time dimension which arises in many scientific and engineering applications such as time series gene expression analysis and video analysis. In these applications, we are interested in determining a set of components interacting closely and consistently together over a period of time. The main aim of this paper is to develop a numerical method to compute such constrained CANDECOMP/PARAFAC (CP) decompositions. We make use of the total variation regularization to constrain the time dimension factor in the decomposition in order to obtain a piecewise constant function with respect to time points. The components of the other dimensions corresponding to these time points are closely related. For example, in time series gene expression analysis, a set of genes may regulate a biological process together during a specific time period; in video analysis, a set of image pixels may refer to a foreground object in the video frames. We employ ADMM to solve the resulting optimization problem, and study its convergence. Numerical examples on synthetic and real data sets are used to demonstrate that the proposed total variation based CP decomposition model can provide more accurate and interesting results.
Persistent Identifierhttp://hdl.handle.net/10722/251136
ISSN
2017 Impact Factor: 1.281
2015 SCImago Journal Rankings: 1.250
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Chuan-
dc.contributor.authorLi, Xutao-
dc.contributor.authorNg, Michael K.-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:42Z-
dc.date.available2018-02-01T01:54:42Z-
dc.date.issued2015-
dc.identifier.citationNumerical Linear Algebra with Applications, 2015, v. 22, n. 6, p. 999-1019-
dc.identifier.issn1070-5325-
dc.identifier.urihttp://hdl.handle.net/10722/251136-
dc.description.abstract© 2015 John Wiley & Sons, Ltd. In this paper, we study tensors with time dimension which arises in many scientific and engineering applications such as time series gene expression analysis and video analysis. In these applications, we are interested in determining a set of components interacting closely and consistently together over a period of time. The main aim of this paper is to develop a numerical method to compute such constrained CANDECOMP/PARAFAC (CP) decompositions. We make use of the total variation regularization to constrain the time dimension factor in the decomposition in order to obtain a piecewise constant function with respect to time points. The components of the other dimensions corresponding to these time points are closely related. For example, in time series gene expression analysis, a set of genes may regulate a biological process together during a specific time period; in video analysis, a set of image pixels may refer to a foreground object in the video frames. We employ ADMM to solve the resulting optimization problem, and study its convergence. Numerical examples on synthetic and real data sets are used to demonstrate that the proposed total variation based CP decomposition model can provide more accurate and interesting results.-
dc.languageeng-
dc.relation.ispartofNumerical Linear Algebra with Applications-
dc.subjectAlternating direction method of multipliers-
dc.subjectRegularization-
dc.subjectTensor decomposition-
dc.subjectTime dimension-
dc.subjectTotal variation-
dc.subjectMultidimensional data-
dc.titleTotal variation based tensor decomposition for multi-dimensional data with time dimension-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1002/nla.1993-
dc.identifier.scopuseid_2-s2.0-84955200728-
dc.identifier.volume22-
dc.identifier.issue6-
dc.identifier.spage999-
dc.identifier.epage1019-
dc.identifier.eissn1099-1506-
dc.identifier.isiWOS:000368371500007-

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