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Article: MR-NTD: Manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation

TitleMR-NTD: Manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation
Authors
Keywordsmanifold learning
Dimension reduction
nonnegative tensors
Issue Date2017
Citation
IEEE Transactions on Neural Networks and Learning Systems, 2017, v. 28, n. 8, p. 1787-1800 How to Cite?
Abstract© 2012 IEEE. With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.
Persistent Identifierhttp://hdl.handle.net/10722/277031
ISSN
2017 Impact Factor: 7.982
2015 SCImago Journal Rankings: 3.181

 

DC FieldValueLanguage
dc.contributor.authorLi, Xutao-
dc.contributor.authorNg, Michael K.-
dc.contributor.authorCong, Gao-
dc.contributor.authorYe, Yunming-
dc.contributor.authorWu, Qingyao-
dc.date.accessioned2019-09-18T08:35:23Z-
dc.date.available2019-09-18T08:35:23Z-
dc.date.issued2017-
dc.identifier.citationIEEE Transactions on Neural Networks and Learning Systems, 2017, v. 28, n. 8, p. 1787-1800-
dc.identifier.issn2162-237X-
dc.identifier.urihttp://hdl.handle.net/10722/277031-
dc.description.abstract© 2012 IEEE. With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.-
dc.languageeng-
dc.relation.ispartofIEEE Transactions on Neural Networks and Learning Systems-
dc.subjectmanifold learning-
dc.subjectDimension reduction-
dc.subjectnonnegative tensors-
dc.titleMR-NTD: Manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1109/TNNLS.2016.2545400-
dc.identifier.pmid28727548-
dc.identifier.scopuseid_2-s2.0-84964573762-
dc.identifier.volume28-
dc.identifier.issue8-
dc.identifier.spage1787-
dc.identifier.epage1800-
dc.identifier.eissn2162-2388-

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