Summary
International Symposium on Nonlinear Theory and Its Applications
2022
Session Number:A6L-B
Session:
Number:A6L-B-01
Spectral Clustering of Directed and Time-Evolving Graphs Using Koopman Operator Theory
Stefan Klus , Natasa Djurdjevac Conrad,
pp.196-196
Publication Date:12/12/2022
Online ISSN:2188-5079
Summary:
Transport networks, electrical grids, and computer networks such as the internet, but also gene regulatory networks, neural networks, and social networks can be represented as directed or undirected graphs by abstracting individual components or entities as nodes and relationships between them as edges. In order to understand such complex networked systems, it is essential to identify community structures or clusters, i.e., sets of nodes that share similar properties. A popular and well-established approach to detect community structures in undirected graphs is spectral clustering. Detecting clusters in directed and time-varying graphs, however, remains a challenging problem. We extend spectral clustering algorithms to directed and time-evolving graphs using transfer operators, which are frequently used to study complex dynamical systems.