Higher-Order Spectral Clustering for Geometric Graphs
This work addresses the challenge of clustering geometric graphs, which standard spectral clustering often fails at, offering a novel method with proven consistency, though it appears incremental as it builds upon classical spectral clustering.
The authors tackled the problem of clustering geometric graphs by introducing higher-order spectral clustering, which uses eigenvectors from higher-order eigenvalues to improve partitioning, and demonstrated its effectiveness through weak and strong consistency proofs and numerical experiments on modest-sized graphs.
The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated with a higher-order eigenvalue. We establish the weak consistency of this algorithm for a wide class of geometric graphs which we call Soft Geometric Block Model. A small adjustment of the algorithm provides strong consistency. We also show that our method is effective in numerical experiments even for graphs of modest size.