Relative Pairwise Relationship Constrained Non-negative Matrix Factorisation

Jiang, S; Li, K; Xu, YDR

Relative Pairwise Relationship Constrained Non-negative Matrix Factorisation

Jiang, S

Li, K Xu, YDR

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Publisher:: Institute of Electrical and Electronics Engineers
Publication Type:: Journal Article
Citation:: IEEE Transactions on Knowledge and Data Engineering, 2019, 31, (8), pp. 1595-1609
Issue Date:: 2019-08-01

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Field	Value	Language
dc.contributor.author	Jiang, S https://orcid.org/0000-0002-5902-9911
dc.contributor.author	Li, K
dc.contributor.author	Xu, YDR
dc.date.accessioned	2020-05-14T02:05:26Z
dc.date.available	2020-05-14T02:05:26Z
dc.date.issued	2019-08-01
dc.identifier.citation	IEEE Transactions on Knowledge and Data Engineering, 2019, 31, (8), pp. 1595-1609
dc.identifier.issn	1041-4347
dc.identifier.issn	1558-2191
dc.identifier.uri	http://hdl.handle.net/10453/140705
dc.description.abstract	IEEE Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering and recommender systems. In this paper, we propose an algorithm named, Relative Pairwise Relationship constrained Non-negative Matrix Factorisation (RPR-NMF), which places constraints over relative pairwise distances amongst features by imposing penalties in a triplet form. Two distance measures, squared Euclidean distance and Symmetric divergence, are used, and exponential and hinge loss penalties are adopted for the two measures respectively. It is well known that the so-called "multiplicative update rules" result in a much faster convergence than gradient descend for matrix factorisation. However, applying such update rules to RPR-NMF and also proving its convergence is not straightforward. Thus, we use reasonable approximations to relax the complexity brought by the penalties, which are practically verified. Experiments on both synthetic datasets and real datasets demonstrate that our algorithms have advantages on gaining close approximation, satisfying a high proportion of expected constraints, and achieving superior performance compared with other algorithms.
dc.language	English
dc.publisher	Institute of Electrical and Electronics Engineers
dc.relation.ispartof	IEEE Transactions on Knowledge and Data Engineering
dc.relation.isbasedon	10.1109/TKDE.2018.2859223
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	08 Information and Computing Sciences
dc.subject.classification	Information Systems
dc.title	Relative Pairwise Relationship Constrained Non-negative Matrix Factorisation
dc.type	Journal Article
utslib.citation.volume	31
utslib.for	08 Information and Computing Sciences
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - INEXT - Innovation in IT Services and Applications
pubs.organisational-group	/University of Technology Sydney/Strength - GBDTC - Global Big Data Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	closed_access	*
pubs.consider-herdc	true
dc.date.updated	2020-05-14T02:05:22Z
pubs.issue	8
pubs.publication-status	Published
pubs.volume	31
utslib.start-page	1595
utslib.citation.issue	8

Abstract:

IEEE Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering and recommender systems. In this paper, we propose an algorithm named, Relative Pairwise Relationship constrained Non-negative Matrix Factorisation (RPR-NMF), which places constraints over relative pairwise distances amongst features by imposing penalties in a triplet form. Two distance measures, squared Euclidean distance and Symmetric divergence, are used, and exponential and hinge loss penalties are adopted for the two measures respectively. It is well known that the so-called "multiplicative update rules" result in a much faster convergence than gradient descend for matrix factorisation. However, applying such update rules to RPR-NMF and also proving its convergence is not straightforward. Thus, we use reasonable approximations to relax the complexity brought by the penalties, which are practically verified. Experiments on both synthetic datasets and real datasets demonstrate that our algorithms have advantages on gaining close approximation, satisfying a high proportion of expected constraints, and achieving superior performance compared with other algorithms.

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http://hdl.handle.net/10453/140705