| Covariance, correlation matrix, and the multiscale community structure of networks. | |
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MedLine Citation:
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PMID: 20866696 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this paper, we consider detecting the multiscale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multiscale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multiscale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix, we further conclude that the rescaling transformation is crucial to identify the multiscale community structure of network, as well as the translation and rotation transformations. |
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Authors:
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Hua-Wei Shen; Xue-Qi Cheng; Bin-Xing Fang |
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Publication Detail:
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Type: Journal Article Date: 2010-07-23 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 82 ISSN: 1550-2376 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2010 Jul |
Date Detail:
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Created Date: 2010-09-27 Completed Date: 2011-01-11 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 016114 Citation Subset: - |
Affiliation:
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Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China. shenhuawei@software.ict.ac.cn |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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