Topological clustering of multilayer networks

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.

ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery

“…TDA and tools of persistent homology (PH) have recently emerged as powerful approaches for ML, allowing us to extract complementary information on the observed objects, especially, from graph-structured data. In particular, PH has become popular for various ML tasks such as clustering, classification, and anomaly detection, with a wide range of applications including material science [68, 43], insurance [99, 46], finance [55], and cryptocurrency analytics [33, 4, 73]. (For more details see surveys [6, 22] and TDA applications library [34]) Furthermore, it has become a highly active research area to integrate PH methods into geometric deep learning (GDL) in recent years [41, 100, 19, 23].…”

Topological Forest

“…Moor et al presented a topological auto-encoder for low-dimensional representation of input data features [42]. Yuvaraj et al used TDA to study complex multilayer networks [43] and to cluster them based on topological approaches, and Bulauan et al [44] clustered complex multilayer networks with topological approaches. Chen et al [45] introduced an approach for measuring the classification boundary of a classifier by using a topological complexity, and Hofer et al [46] developed topological constraint to improve the generalization performance of their model.…”

Community detection in complex networks: From statistical foundations to data science applications

“…Hence, we now deal with community detection not in a single network but in a network of networks , requiring to exploit and fuse multiple aspects of disparate, yet interdependent sources of information. While some community detection methods discussed in the previous sections can be extended to the analysis of multilayer networks, extracting multilayer communities poses many new challenges due to nontrivial heterogeneous interlayer and intralayer dependencies and yet remains a substantially less developed area in complex network analysis (Amelio et al, 2020; Contisciani et al, 2020; Yuvaraj et al, 2021). Figure 9 shows a schematic representation of communities in a multilayer network.…”