Fast online graph clustering via Erdős–Rényi mixture

Zanghi, Hugo; Ambroise, Christophe; Miele, Vincent

doi:10.1016/j.patcog.2008.06.019

Cited by 89 publications

(76 citation statements)

References 25 publications

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“…Zanghi et al (Zanghi et al, 2008) have designed a clustering technique that lies somewhat in between the method by Hastings and that by Newman and Leicht. As in (Hastings, 2006), they use the planted partition model to represent a graph with community structure; as in (Newman and Leicht, 2007), they maximize the classification likelihood using an expectation-maximization algorithm (Dempster et al, 1977).…”

Section: A Generative Modelsmentioning

confidence: 99%

Community detection in graphs

2010

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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Section: A Generative Modelsmentioning

confidence: 99%

Community detection in graphs

2010

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“…If the system is large and its structure is updated in a stream fashion, instead of working on snapshots one could detect the clustering online, every time the configuration of the system varies due to new information, like the addition of a new vertex or edge (Aggarwal and Philip, 2005;Zanghi et al, 2008). An advantage of this approach is that change is due to the effect that the small variation in the network structure has on the system, and it can be tracked by simply adjusting the partition of the previous configuration, which can be usually done rather quickly.…”

Section: H Dynamic Clusteringmentioning

confidence: 99%

Community detection in networks: A user guide

2016

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Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other groups, though other patterns are possible. Identifying communities is an ill-defined problem. There are no universal protocols on the fundamental ingredients, like the definition of community itself, nor on other crucial issues, like the validation of algorithms and the comparison of their performances. This has generated a number of confusions and misconceptions, which undermine the progress in the field. We offer a guided tour through the main aspects of the problem. We also point out strengths and weaknesses of popular methods, and give directions to their use.

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“…This Classification EM (CEM) approach has been subject to previous work (Zanghi et al (2007)). It gives biased estimates but is very efficient in terms of computational cost.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…Indeed, many scientific fields such as biology (Albert and Barabási (2002)), social science, and information technology, see those mathematical strutures as powerful tools to model the interactions between objects of interest. Examples of data sets having such structures are friendship (Palla et al (2007)) and protein-protein interaction networks (Barabási and Oltvai (2004)), powergrids (Watts and Strogatz (1998)), and the Internet (Zanghi et al (2007)). In this context, a lot of attention has been paid on developing models to learn knowledge from the network topology.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Methods for Graph Clustering

Latouche¹,

Birmelé²,

Ambroise³

2009

Studies in Classification, Data Analysis, and Knowledge Organization

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Networks are used in many scientific fields such as biology, social science, and information technology. They aim at modelling, with edges, the way objects of interest, represented by vertices, are related to each other. Looking for clusters of vertices, also called communities or modules, has appeared to be a powerful approach for capturing the underlying structure of a network. In this context, the Block-Clustering model has been applied on random graphs. The principle of this method is to assume that given the latent structure of a graph, the edges are independent and generated from a parametric distribution. Many EM-like strategies have been proposed, in a frequentist setting, to optimize the parameters of the model. Moreover, a criterion, based on an asymptotic approximation of the Integrated Classification Likelihood (ICL), has recently been derived to estimate the number of classes in the latent structure. In this paper, we show how the Block-Clustering model can be described in a full Bayesian framework and how the posterior distribution, of all the parameters and latent variables, can be approximated efficiently applying Variational Bayes (VB). We also propose a new non-asymptotic Bayesian model selection criterion. Using simulated and real data sets, we compare our approach to other strategies. We show that our Bayesian method is able to handle large networks and that our criterion is more robust than ICL.

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Fast online graph clustering via Erdős–Rényi mixture

Cited by 89 publications

References 25 publications

Community detection in graphs

Community detection in graphs

Community detection in networks: A user guide

Bayesian Methods for Graph Clustering

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