Identifying the Topology of Undirected Networks From Diffused Non-Stationary Graph Signals

We address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary signals generated by local diffusion dynamics that depend on structure unknown network. Using so-called graph-shift operator (GSO), is a matrix representation graph, we first identify eigenvectors shift observations diffused signals, and then estimate eigenvalues imposing desirable properties to be recovered. Different stationary setting where can obtained directly covariance measurements, here need (graph) filter - polynomial in GSO preserves sought eigenbasis. To carry out this initial system identification step, exploit different sources information arbitrarily-correlated input signal driving graph. explore information, linearly related. case relation given quadratic equations, arises pragmatic scenarios only second-order statistics inputs available. While such boils down non-convex fourth-order minimization, discuss identifiability conditions, propose algorithms approximate solution, analyze their performance. Numerical tests illustrate effectiveness proposed topology inference recovering brain, social, financial, urban transportation networks using synthetic real-world signals.