2023/03/14 by Thummaluru Siddartha Reddy, Reddy, Thummaluru Siddartha, Sundeep Prabhakar Chepuri +3
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Graph theory and applications #Machine Learning (cs.LG) #Signal Processing (eess.SP) #Topological and Geometric Data Analysis #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2303.07646
openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.