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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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. © 2023 European Signal Processing Conference, EUSIPCO. All rights reserved.
| Item Type: | Conference Paper |
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| 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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