Benefits of Hypergraphs for Density-Based Clustering
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| Názov: | Benefits of Hypergraphs for Density-Based Clustering |
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| Autori: | Hauseux, Louis, Avrachenkov, Konstantin, Zerubia, Josiane |
| Prispievatelia: | Hauseux, Louis |
| Zdroj: | 2024 32nd European Signal Processing Conference (EUSIPCO). :2302-2306 |
| Informácie o vydavateľovi: | IEEE, 2024. |
| Rok vydania: | 2024 |
| Predmety: | percolation, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], hypergraphs, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, geometric graphs, density estimator, [INFO] Computer Science [cs], hierarchical clustering |
| Popis: | 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. |
| Druh dokumentu: | Article Conference object |
| Popis súboru: | application/pdf |
| DOI: | 10.23919/eusipco63174.2024.10715271 |
| Rights: | STM Policy #29 CC BY NC |
| Prístupové číslo: | edsair.doi.dedup.....d9e2fa01c6bdfe6057e5a7b9d402b5cb |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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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| DOI: | 10.23919/eusipco63174.2024.10715271 |