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

• Published in: Journal of computer science and technology Vol. 27; no. 2; pp. 341 - 357
• Main Author: 沈华伟 程学旗 王元卓 陈一昕
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.03.2012; Springer Nature B.V; Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China%Computer Science Department,Washington University in St Louis,MO 63130,U.S.A
• Subjects: Algorithms; Analysis; Artificial Intelligence; Clustering; Communities; Computer Science; Data Structures and Information Theory; Eigenvalues; Graph representations; Graph theory; Information Systems Applications (incl.Internet); Laplace transforms; Laplacian; Mathematical analysis; Matrices; Matrix methods; Methods; Modularity; Network topologies; Networks; Principal components analysis; Reduction; Regular Paper; Science; Software Engineering; Studies; Theory of Computation; Topology; 协方差矩阵; 多尺度结构; 异构网络; 框架; 社会结构; 角度检测; 降维; dimensionality reduction; Laplacian matrix; community structure; modularity matrix; graph clustering
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-012-1227-y

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.