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A Dimensionality Reduction Framework for Detection of Multiscale Structure in Heterogeneous Networks

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Abstract

Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks.

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Authors and Affiliations

  1. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Hua-Wei Shen (Member, CCF), Xue-Qi Cheng (Senior Member, CCF, Member, IEEE) & Yuan-Zhuo Wang (Senior Member, CCF, Member, ACM, IEEE)

  2. Computer Science Department, Washington University, St Louis, MO, 63130, U.S.A.

    Yixin Chen (Senior Member, IEEE)

Authors
  1. Hua-Wei Shen
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  2. Xue-Qi Cheng
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  3. Yuan-Zhuo Wang
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  4. Yixin Chen
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Corresponding author

Correspondence to Hua-Wei Shen.

Additional information

This work was funded by the National Natural Science Foundation of China under Grant Nos. 60873245, 60933005, 60873243, 60903139 and 60803123. This work was also partly funded by the National High Technology Research and Development 863 Program of China under Grant No. 2010AA012503, and the Beijing Natural Science Foundation under Grant No. 4122077.

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Shen, HW., Cheng, XQ., Wang, YZ. et al. A Dimensionality Reduction Framework for Detection of Multiscale Structure in Heterogeneous Networks. J. Comput. Sci. Technol. 27, 341–357 (2012). https://doi.org/10.1007/s11390-012-1227-y

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