source: arxiv statistics ml: directed graph topology inference via graph filter identification
level: research
this work tackles the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics. the observations come from a graph convolutional filter, which is a polynomial of a local diffusion operator that encodes the hidden graph structure. the filter is excited by independent graph signals with arbitrarily correlated nodal components. unlike previous work that assumed undirected graphs and white noise inputs, here the graph shift operator and the observation covariance matrix cannot be diagonalized at the same time.
the approach first uses output signal measurements and prior statistical information about the inputs to identify the diffusion filter. this system identification step requires solving a system of quadratic matrix equations. the authors show that the filter is identifiable under a spectral diversity condition, meaning the input signals have sufficiently varied spectral content. once the filter is known, the graph topology can be recovered from the filter coefficients.
the method handles the challenging case where the graph is directed and the input signals are not white. this is important because many real-world networks, such as social or biological networks, are directed and have correlated node activities. the technique could improve network analysis in fields like neuroscience, where directed connectivity matters, or in infrastructure monitoring where diffusion processes are common.
why it matters: it enables learning directed network structures from real-world diffusion data, which is common in ai applications like brain connectivity analysis and sensor networks.
source: arxiv statistics ml: directed graph topology inference via graph filter identification