Community detection in trajectory networks and simplicial complexes for extracting patterns in complex data
- Sanjukta Krishnagopal (Gatsby Computational Neuroscience Unit)
Community detection in complex networks has been very successful in understanding several systems where interactions are inherent. First, I introduce a novel trajectory-based method for identifying and predicting subtypes in heterogeneous and longitudinal data, i.e., that are characterized by time-varying interactions between various factors. The conventional Laplacian encodes many dynamical properties of a network, including community structure and flow of information along the network. Through spectral community detection in the graphical domain, I perform community detection on trajectory-based networks, for the application of identifying and predicting subtypes of diseases several years in advance.
While networks are a useful tool to represent data in the graphical domain, most systems naturally evolve to contain simultaneous interactions between more than two entities, represented as simplices - triangles, tetrahedra etc. Here I present the first work on revealing the relationship between a higher order equivalent of the Laplacian (Hodge Laplacian) and higher-order simplicial communities, demonstrating our results on both synthetic networks, as well as social and language networks.
I discuss the implications of Hodge decomposition on simplicial communities, and their relationship with clique communities. Lastly, I present a method to infer higher-order simplicial complexes from the network backbone, a question of some importance as simplicial datasets are rare.