Cluster Persistence for Weighted Graphs

Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology. While this area has been thoroughly studied, we present a new approach to constructing a filtration for cluster analysis via persistent homology...

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Veröffentlicht in:Entropy (Basel, Switzerland) Switzerland), 2023-11, Vol.25 (12), p.1587
Hauptverfasser: Bobrowski, Omer, Skraba, Primoz
Format: Artikel
Sprache:eng
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Zusammenfassung:Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology. While this area has been thoroughly studied, we present a new approach to constructing a filtration for cluster analysis via persistent homology. The key advantages of the new filtration is that (a) it provides richer signatures for connected components by introducing non-trivial birth times, and (b) it is robust to outliers. The key idea is that nodes are ignored until they belong to sufficiently large clusters. We demonstrate the computational efficiency of our filtration, its practical effectiveness, and explore into its properties when applied to random graphs.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25121587