Exploring the structural regularities in networks

Shen, Huawei; Cheng, Xueqi; Guo, Jiafeng

doi:10.1103/physreve.84.056111

Cited by 63 publications

(66 citation statements)

References 31 publications

(55 reference statements)

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“…One possible solution is to adopt an iterative self-consistent approach that evaluates both simultaneously. Like many previous works [11,[23][24][25], we utilize the expectationmaximization (EM) algorithm, which first computes the posterior probabilities of hidden variables using estimated model parameters and observed data (the E-step), and then re-estimates the model parameters (the Mstep).…”

Section: A the Ssbm Modelmentioning

confidence: 99%

Stochastic block model and exploratory analysis in signed networks

Jiang

2015

Phys. Rev. E

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We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group memberships are viewed as hidden or unobserved quantities, and the connection patterns between groups are explicitly characterized by two block matrices, one for positive links and the other for negative links. By fitting the model to the observed network, we can not only extract various structural patterns existing in the network without prior knowledge, but also recognize what specific structures we obtained. Furthermore, the model parameters provide vital clues about the probabilities that each vertex belongs to different groups and the centrality of each vertex in its corresponding group. This information sheds light on the discovery of the networks overlapping structures and the identification of two types of important vertices, which serve as the cores of each group and the bridges between different groups, respectively. Experiments on a series of synthetic and real-life networks show the effectiveness as well as the superiority of our model.

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Section: A the Ssbm Modelmentioning

confidence: 99%

Stochastic block model and exploratory analysis in signed networks

Jiang

2015

Phys. Rev. E

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“…In this section, we first review two related link models, i.e., the GSB model [17] and the PPL model [21], whose graphical models are shown in Fig. 1.…”

Section: A Related Link Modelsmentioning

confidence: 99%

“…The plate models for network data: (a) the GSB model proposed in [17] and (b) the PPL model proposed in [21]. Shaded circles represent observed variables, and unshaded ones correspond to latent variables.…”

Section: A Related Link Modelsmentioning

confidence: 99%

“…One category models the joint link probability based on the idea of link community. This category is roughly put into two kinds: (1) models for general structure detection, including the mixed membership stochastic block (MMB) model [15], the interaction Dirichlet block model (IDBM) [16], and the general stochastic block (GSB) model [17], and (2) models for traditional community detection, including the simple probabilistic algorithm for community detection employing expectation-maximization (SPAEM) [18], the Bayesian link model [19], the generative model for link community [20], the popularity and productivity link (PPL) model [21], etc. [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection

Chai

Jia

et al. 2013

Phys. Rev. E

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Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.

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“…Many methods have been proposed and applied successfully to some specific complex networks [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . For survey and comparison, the reader can refer to [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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

Shen

Cheng

Wang

et al. 2012

J. Comput. Sci. Technol.

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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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Exploring the structural regularities in networks

Cited by 63 publications

References 31 publications

Stochastic block model and exploratory analysis in signed networks

Stochastic block model and exploratory analysis in signed networks

Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection

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

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