Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs
This work addresses the under-researched problem of mesoscale structure detection in higher-order networks, which is important for analyzing complex systems like social or transportation networks, but it is incremental as it builds on existing higher-order network models.
The paper tackled the problem of detecting mesoscale structures in pathway data on graphs, where interactions have dependencies, by deriving a Bayesian approach that simultaneously models node partitioning and higher-order network dynamics; the result showed that the method can recover both proximity-based communities and role-based groupings in synthetic data and compete with baseline techniques in synthetic and real-world data.
Mesoscale structures are an integral part of the abstraction and analysis of complex systems. They reveal a node's function in the network, and facilitate our understanding of the network dynamics. For example, they can represent communities in social or citation networks, roles in corporate interactions, or core-periphery structures in transportation networks. We usually detect mesoscale structures under the assumption of independence of interactions. Still, in many cases, the interactions invalidate this assumption by occurring in a specific order. Such patterns emerge in pathway data; to capture them, we have to model the dependencies between interactions using higher-order network models. However, the detection of mesoscale structures in higher-order networks is still under-researched. In this work, we derive a Bayesian approach that simultaneously models the optimal partitioning of nodes in groups and the optimal higher-order network dynamics between the groups. In synthetic data we demonstrate that our method can recover both standard proximity-based communities and role-based groupings of nodes. In synthetic and real world data we show that it can compete with baseline techniques, while additionally providing interpretable abstractions of network dynamics.