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Eigenvector Computation and Community Detection in Asynchronous Gossip Models

Authors Frederik Mallmann-Trenn, Cameron Musco, Christopher Musco

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ACM Subject Classification
  • Computing methodologies → Distributed algorithms
Keywords
  • block model
  • community detection
  • distributed clustering
  • eigenvector computation
  • gossip algorithms
  • population protocols

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Abstract

We give a simple distributed algorithm for computing adjacency matrix eigenvectors for the communication graph in an asynchronous gossip model. We show how to use this algorithm to give state-of-the-art asynchronous community detection algorithms when the communication graph is drawn from the well-studied stochastic block model. Our methods also apply to a natural alternative model of randomized communication, where nodes within a community communicate more frequently than nodes in different communities.
Our analysis simplifies and generalizes prior work by forging a connection between asynchronous eigenvector computation and Oja's algorithm for streaming principal component analysis. We hope that our work serves as a starting point for building further connections between the analysis of stochastic iterative methods, like Oja's algorithm, and work on asynchronous and gossip-type algorithms for distributed computation.

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Frederik Mallmann-Trenn, Cameron Musco, and Christopher Musco. Eigenvector Computation and Community Detection in Asynchronous Gossip Models. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 159:1-159:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.159

Author Details

Frederik Mallmann-Trenn
  • CSAIL, MIT, US
Cameron Musco
  • CSAIL, MIT, US
Christopher Musco
  • CSAIL, MIT, US

Funding

This work was supported in part by NSF Award Numbers BIO-1455983, CCF-1461559, CCF-0939370, and CCF-1565235. Cameron Musco was partially supported by an NSF graduate student fellowship.

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