Clustering with Simplicial Complexes

Understand

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.