Cluster Persistence for Weighted Graphs

Author:

Bobrowski Omer12ORCID,Skraba Primoz13

Affiliation:

1. School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK

2. Viterbi Faculty of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel

3. Department for Artificial Intelligence, Jozef Stefan Institute, 1000 Ljubljana, Slovenia

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 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.

Funder

Israel Science Foundation

EU project EnRichMyData

Publisher

MDPI AG

Subject

General Physics and Astronomy

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