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 c...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.展开更多
基金funded by the National Natural Science Foundation of China under Grant Nos. 60873245,60933005,60873243,60903139 and 60803123funded by the National High Technology Research and Development 863 Programof China under Grant No. 2010AA012503the Beijing Natural Science Foundation under Grant No. 4122077
文摘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.
