Cluster-Persistence for Weighted Graphs

Omer Bobrowski; Primoz Skraba

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arXiv · 2310.00350

Cluster-Persistence for Weighted Graphs

Omer Bobrowski·Primoz Skraba

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Abstract

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 substantially 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.

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Omer Bobrowski, Primoz Skraba. 2023-09-30. Cluster-Persistence for Weighted Graphs. https://arxiv.org/abs/2310.00350

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