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A simpler spectral approach for clustering in directed networks

Simon Coste

Abstract

We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD truncation, and works very well down to the very sparse regime where the edge density has constant order. This simple approach was largely unnoticed in the mathematics and network science communities. Our analysis is based on a Master Theorem describing sharp asymptotics for isolated eigenvalues/eigenvectors of sparse, non-symmetric matrices with independent entries. We also describe the limiting distribution of the entries of these eigenvectors; in the task of digraph clustering with spectral embeddings, we provide numerical evidence for the superiority of Gaussian Mixture clustering over the widely used k-means algorithm.

Dates and versions

hal-03137583 , version 1 (10-02-2021)

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Simon Coste, Ludovic Stephan. A simpler spectral approach for clustering in directed networks. 2021. ⟨hal-03137583⟩
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