Covariance, correlation matrix, and the multiscale community structure of networks

doi:10.1103/PhysRevE.82.016114

	Covariance, correlation matrix, and the multiscale community structure of networks
	Shen, Hua-Wei; Cheng, Xue-Qi; Fang, Bin-Xing
	2010-07-23
发表期刊	PHYSICAL REVIEW E
ISSN	1539-3755
卷号	82 期号:1 页码:9
摘要	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.
DOI	10.1103/PhysRevE.82.016114
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[60873245] ; National Natural Science Foundation of China[60933005]
WOS研究方向	Physics
WOS类目	Physics, Fluids & Plasmas ; Physics, Mathematical
WOS记录号	WOS:000280233700002
出版者	AMER PHYSICAL SOC
引用统计	被引频次：39[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/12499
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Shen, Hua-Wei
作者单位	Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Shen, Hua-Wei,Cheng, Xue-Qi,Fang, Bin-Xing. Covariance, correlation matrix, and the multiscale community structure of networks[J]. PHYSICAL REVIEW E,2010,82(1):9.
APA	Shen, Hua-Wei,Cheng, Xue-Qi,&Fang, Bin-Xing.(2010).Covariance, correlation matrix, and the multiscale community structure of networks.PHYSICAL REVIEW E,82(1),9.
MLA	Shen, Hua-Wei,et al."Covariance, correlation matrix, and the multiscale community structure of networks".PHYSICAL REVIEW E 82.1(2010):9.