The Geometric Block Model

Authors

  • Sainyam Galhotra University of Massachusetts Amherst
  • Arya Mazumdar University of Massachusetts Amherst
  • Soumyabrata Pal University of Massachusetts Amherst
  • Barna Saha University of Massachusetts Amherst

DOI:

https://doi.org/10.1609/aaai.v32i1.11905

Abstract

To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric graphs in the same way that the well-studied stochastic block model generalizes the Erdös-Renyi random graphs. It is also a natural extension of random community models inspired by the recent theoretical and practical advancement in community detection. While being a topic of fundamental theoretical interest, our main contribution is to show that many practical community structures are better explained by the geometric block model. We also show that a simple triangle-counting algorithm to detect communities in the geometric block model is near-optimal. Indeed, even in the regime where the average degree of the graph grows only logarithmically with the number of vertices (sparse-graph), we show that this algorithm performs extremely well, both theoretically and practically. In contrast, the triangle-counting algorithm is far from being optimum for the stochastic block model. We simulate our results on both real and synthetic datasets to show superior performance of both the new model as well as our algorithm.

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Published

2018-04-26

How to Cite

Galhotra, S., Mazumdar, A., Pal, S., & Saha, B. (2018). The Geometric Block Model. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1). https://doi.org/10.1609/aaai.v32i1.11905

Issue

Section

Main Track: Machine Learning Applications