A simpler spectral approach for clustering in directed networks

• URL: http://arxiv.org/abs/2102.03188v1
• Date: Fri, 5 Feb 2021 14:16:45 GMT
• Title: A simpler spectral approach for clustering in directed networks
• Authors: Simon Coste and Ludovic Stephan
• Abstract summary: We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods. We provide numerical evidence for the superiority of the Gaussian Mixture clustering over the widely used k-means algorithm.
• Score: 1.52292571922932
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 well down to the very sparse regime where the edge density has constant order. 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.

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