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CLUSTERED MATRIX APPROXIMATION
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1542-2690
University of Texas Austin, USA.
2016 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 37, no 4, p. 1531-1555Article in journal (Refereed) Published
Abstract [en]

In this paper we develop a novel clustered matrix approximation framework, first showing the motivation behind our research. The proposed methods are particularly well suited for problems with large scale sparse matrices that represent graphs and/or bipartite graphs from information science applications. Our framework and resulting approximations have a number of benefits: (1) the approximations preserve important structure that is present in the original matrix; (2) the approximations contain both global-scale and local-scale information; (3) the procedure is efficient both in computational speed and memory usage; and (4) the resulting approximations are considerably more accurate with less memory usage than truncated SVD approximations, which are optimal with respect to rank. The framework is also quite flexible as it may be modified in various ways to fit the needs of a particular application. In the paper we also derive a probabilistic approach that uses randomness to compute a clustered matrix approximation within the developed framework. We further prove deterministic and probabilistic bounds of the resulting approximation error. Finally, in a series of experiments we evaluate, analyze, and discuss various aspects of the proposed framework. In particular, all the benefits we claim for the clustered matrix approximation are clearly illustrated using real-world and large scale data.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2016. Vol. 37, no 4, p. 1531-1555
Keywords [en]
matrix approximation; dimensionality reduction; low rank matrix approximation; probabilistic algorithms; graph mining; social network analysis; clustering; coclustering
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-134533DOI: 10.1137/15M1042206ISI: 000391857300008OAI: oai:DiVA.org:liu-134533DiVA, id: diva2:1074287
Note

Funding Agencies|Vetenskapsradet [2008:7145]; National Science Foundation (NSF) [CCF-1320746, CCF-1117055]

Available from: 2017-02-15 Created: 2017-02-15 Last updated: 2017-11-29

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