Data fusion reconstruction of spatially embedded complex networks

We introduce a kernel Lasso (kLasso) approach which is a type of sparse optimization that simultaneously accounts for spatial regularity and structural sparsity to reconstruct spatially embedded complex networks from time-series data about nodal states. Through the design of a spatial kernel function motivated by real-world network features, the proposed kLasso approach exploits spatial embedding distances to penalize overabundance of spatially long-distance connections. Examples of both random geometric graphs and real-world transportation networks show that the proposed method improves significantly upon existing network reconstruction techniques that mainly concern sparsity but not spatial regularity. Our results highlight the promise of data and information fusion in the reconstruction of complex networks, by utilizing both microscopic node-level dynamics (e.g. time series data) and macroscopic network-level information (metadata or other prior information).