This work is devoted to clustering geometric graphs. It appears that 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.
This is a joint work with A. Bobu and M. Dreveton, done in the framework of Inria – Nokia Bell Labs and recently appeared in JFAA, 27:22, 2021.