Improved spectral community detection in large heterogeneous networks

Abstract : In this article, we propose and study the performance of spectral community detection for a family of "α-normalized" adjacency matrices A, of the type D −α AD −α with D the degree matrix, in heterogeneous dense graph models. We show that the previously used normaliza-tion methods based on A or D −1 AD −1 are in general suboptimal in terms of correct recovery rates and, relying on advanced random matrix methods, we prove instead the existence of an optimal value α opt of the parameter α in our generic model; we further provide an online estimation of α opt only based on the node degrees in the graph. Numerical simulations show that the proposed method outperforms state-of-the-art spectral approaches on moderately dense to dense heterogeneous graphs.
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Submitted on : Monday, December 17, 2018 - 2:38:14 PM
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Hafiz Tiomoko Ali, Romain Couillet. Improved spectral community detection in large heterogeneous networks. Journal of Machine Learning Research, Journal of Machine Learning Research, 2018, 18 (10), pp.1-49. ⟨http://www.jmlr.org/papers/v18/17-247.html⟩. ⟨hal-01957623⟩

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