Clustering with Simplicial Complexes
Abstract
In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on minimizing, yields an optimal partition with a higher density of filled triangles within the set while the density of filled triangles is smaller across the sets. To this end, we propose a simplicial adjacency operator that captures the relation between the nodes through second-order simplices. This allows us to extend the well-known Cheeger inequality to cluster a simplicial complex. Then, leveraging the Cheeger inequality, we propose the simplicial spectral clustering algorithm. We report results from numerical experiments on synthetic and real-world network data to demonstrate the efficacy of the proposed approach.
Cite
@article{arxiv.2303.07646,
title = {Clustering with Simplicial Complexes},
author = {Thummaluru Siddartha Reddy and Sundeep Prabhakar Chepuri and Pierre Borgnat},
journal= {arXiv preprint arXiv:2303.07646},
year = {2023}
}