Topological Clustering of Multilayer Networks

Music City Center 

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 socio-environmental ecosystems. However, the clustering of multilayer networks, especially, using the information on higher order interactions of the system entities, yet 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 talk we introduce the concepts of Topological Data Analysis (TDA) to studies of complex multilayer networks and propose a new 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 the topological summary, termed persistence diagrams, we refer to the new 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 in application to 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.

clustering

topological machine learning

topological and geometric methods in statistics