Topological clustering of multilayer networks

Monisha Yuvaraj, Asim K. Dey, Vyacheslav Lyubchich, Yulia R. Gel, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.

Original languageEnglish (US)
Article numbere2019994118
JournalProceedings of the National Academy of Sciences of the United States of America
Volume118
Issue number21
DOIs
StatePublished - May 25 2021

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Clustering
  • Insurance risk
  • Multilayer network
  • Persistence diagram
  • Topological data analysis

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