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Conference Papers Year : 2024

Benefits of hypergraphs for density-based clustering

Abstract

Many of clustering algorithms are based on density estimates in R^d . Building geometric graphs on the dataset X is an elegant way of doing this. In fact, the connected components of a geometric graph match exactly with the high-density clusters of the 1-Nearest Neighbor density estimator. In this paper, We show that the natural way to generalize geometric graphs is to use hypergraphs with a more restrictive notion of connected component called K-Polyhedron. Herein, we prove that K-polyhedra correspond to high-density clusters of K-Nearest Neighbors density estimator. Furthermore, the percolation phenomenon is omnipresent behind the family of clustering algorithms we look at in this paper.
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hal-04617936 , version 1 (19-06-2024)

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  • HAL Id : hal-04617936 , version 1

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Louis Hauseux, Konstantin Avrachenkov, Josiane Zerubia. Benefits of hypergraphs for density-based clustering. EUSIPCO 2024 - 32nd IEEE European Signal Processing Conference, Aug 2024, Lyon, France. ⟨hal-04617936⟩
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