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Clustering with Simplicial Complexes

Reddy, TS and Chepuri, SP and Borgnat, P (2023) Clustering with Simplicial Complexes. In: 31st European Signal Processing Conference, EUSIPCO 2023, 4 - 8 September 2023, Helsinki, pp. 1609-1613.

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Official URL: https://doi.org/10.23919/EUSIPCO58844.2023.1028974...


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. © 2023 European Signal Processing Conference, EUSIPCO. All rights reserved.

Item Type: Conference Paper
Publication: European Signal Processing Conference
Publisher: European Signal Processing Conference, EUSIPCO
Additional Information: The copyright for this article belongs to Author.
Keywords: Clustering algorithms; Signal processing, Cheeger inequalities; Clusterings; High-order; High-order cut; Higher-order; In networks; New clustering algorithms; Second orders; Simplicial complex; Triangle conductance, Complex networks
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 01 Mar 2024 05:32
Last Modified: 01 Mar 2024 05:32
URI: https://eprints.iisc.ac.in/id/eprint/83794

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