Community recovery in non-binary and temporal stochastic block models

Avrachenkov, Konstantin; Dreveton, Maximilien; Leskelä, Lasse

doi:10.48550/arxiv.2008.04790

Cited by 3 publications

(8 citation statements)

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“…Specialised to T = 1, Theorem 2 also improves the result of [6] who showed that I 1 ≥ (4 + δ) log N N is sufficient for posterior exact recovery in single-layer networks. In a frequentist setting, [18] presents consistency thresholds for multilayer SBMs, which are comparable to those of Theorems 1 and 2.…”

Section: Resultssupporting

confidence: 63%

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Consistent Bayesian community recovery in multilayer networks

Alaluusua¹,

Leskelä²

2022

Preprint

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Revealing underlying relations between nodes in a network is one of the most important tasks in network analysis. Using tools and techniques from a variety of disciplines, many community recovery methods have been developed for different scenarios. Despite the recent interest on community recovery in multilayer networks, theoretical results on the accuracy of the estimates are few and far between. Given a multilayer, e.g. temporal, network and a multilayer stochastic block model, we derive bounds for sufficient separation between intra-and inter-block connectivity parameters to achieve posterior exact and almost exact community recovery. These conditions are comparable to a well known threshold for community detection by a single-layer stochastic block model. A simulation study shows that the derived bounds translate to classification accuracy that improves as the number of observed layers increases.

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Section: Resultssupporting

confidence: 63%

“…a three-way adjacency tensor indexed by nodes and a time parameter. Despite recent interest, the number of theoretical results in this direction has so far been rather limited [13,14,15,16,17,18]. In particular, there exists little research on Bayesian consistency for multilayer network models.…”

Section: Introductionmentioning

confidence: 99%

Consistent Bayesian community recovery in multilayer networks

Alaluusua¹,

Leskelä²

2022

Preprint

Self Cite

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“…The following proposition, whose proof can be found in (Avrachenkov et al, 2022), states recovery conditions for a sparse Markov SBM when n 1 and T 1. The notions of consistent and strongly consistent estimators were defined in Section 4.4.3.…”

Section: Recovery Thresholds In Sbm With Markov Interactionmentioning

confidence: 99%

“…The quantity ρT Ĩ corresponds to the main term in the Taylor expansion of the Rényi divergence between two Markov chain distributions f in and f out . We refer to (Avrachenkov et al, 2022) for more details and proofs. Remark 6.1.…”

Section: Recovery Thresholds In Sbm With Markov Interactionmentioning

confidence: 99%

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Statistical Analysis of Networks

Avrachenkov

Dreveton

2022

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This book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Many fundamental modern tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms.Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to the statistical approach to the analysis of complex networks.In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition "à la carte". Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also useful to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7.As prerequisites for reading our book, we expect basic knowledge in probability, linear algebra and elementary notions of graph theory. We have also added appendices describing some required notions from the above mentioned disciplines.

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The projection method: a unified formalism for community detection

Gösgens,

van der Hofstad,

Litvak

2024

Front. Complex Syst.

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We present the class of projection methods for community detection that generalizes many popular community detection methods. In this framework, we represent each clustering (partition) by a vector on a high-dimensional hypersphere. A community detection method is a projection method if it can be described by the following two-step approach: 1) the graph is mapped to a query vector on the hypersphere; and 2) the query vector is projected on the set of clustering vectors. This last projection step is performed by minimizing the distance between the query vector and the clustering vector, over the set of clusterings. We prove that optimizing Markov stability, modularity, the likelihood of planted partition models and correlation clustering fit this framework. A consequence of this equivalence is that algorithms for each of these methods can be modified to perform the projection step in our framework. In addition, we show that these different methods suffer from the same granularity problem: they have parameters that control the granularity of the resulting clustering, but choosing these to obtain clusterings of the desired granularity is nontrivial. We provide a general heuristic to address this granularity problem, which can be applied to any projection method. Finally, we show how, given a generator of graphs with community structure, we can optimize a projection method for this generator in order to obtain a community detection method that performs well on this generator.

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Community recovery in non-binary and temporal stochastic block models

Cited by 3 publications

References 0 publications

Consistent Bayesian community recovery in multilayer networks

Consistent Bayesian community recovery in multilayer networks

Statistical Analysis of Networks

The projection method: a unified formalism for community detection

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