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Communication Dans Un Congrès Année : 2023

Clustering with Simplicial Complexes

Résumé

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 secondorder 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. *
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Dates et versions

hal-04227080 , version 1 (03-10-2023)

Identifiants

  • HAL Id : hal-04227080 , version 1

Citer

Thummaluru Siddartha Reddy, Sundeep Prabhakar Chepuri, Pierre. Borgnat. Clustering with Simplicial Complexes. EUSIPCO 2023, 31st European Signal Processing Conference, EURASIP, European Association for Signal Processing, Sep 2023, Helsinki, Finland. ⟨hal-04227080⟩
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