Pseudo-likelihood methods for community detection in large sparse networks

@article{Amini2012PseudolikelihoodMF,
  title={Pseudo-likelihood methods for community detection in large sparse networks},
  author={Arash A. Amini and Aiyou Chen and Peter J. Bickel and Elizaveta Levina},
  journal={Annals of Statistics},
  year={2012},
  volume={41},
  pages={2097-2122}
}
Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the… 
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References

SHOWING 1-10 OF 42 REFERENCES

An efficient and principled method for detecting communities in networks

This work describes a method for finding overlapping communities based on a principled statistical approach using generative network models and shows how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times.

Spectral clustering and the high-dimensional stochastic blockmodel

The asymptotic results in th is paper are the first clustering results that allow the number of clusters in the model to grow with theNumber of nodes, hence the name high-dimensional.

Stochastic blockmodels and community structure in networks

  • B. KarrerM. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
This work demonstrates how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks and proposes a heuristic algorithm forcommunity detection using this objective function or its non-degree-corrected counterpart.

Null models for network data

This work shows how the logistic-linear model and the implicit log- linear model may be viewed as instances of a broader class of null models, with the property that all members of this class give rise to essentially the same likelihood-based estimates of link probabilities in sparse graph regimes.

Consistency of community detection in networks under degree-corrected stochastic block models

It is found that methods based on the degree-corrected stochastic block model are consistent under a wider class of models and that modularity-type methods require parameter constraints for consistency, whereas likelihood-based methods do not.

Detecting community structure in networks

A number of more recent algorithms that appear to work well with real-world network data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks are described.

Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

This paper uses the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram of the stochastic block model, a commonly used generative model for social and biological networks, and develops a belief propagation algorithm for inferring functional groups or communities from the topology of the network.

Mixture models and exploratory analysis in networks

A general technique for detecting structural features in large-scale network data that works by dividing the nodes of a network into classes such that the members of each class have similar patterns of connection to other nodes is described.

Uncovering latent structure in valued graphs: A variational approach

This work presents a model-based strategy to uncover groups of nodes in valued graphs that can be used for a wide span of parametric random graphs models and allows to include covariates.

Finding and evaluating community structure in networks.

  • M. NewmanM. Girvan
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.