Blind Community Detection from Low-rank Excitations of a Graph Filter
This addresses community detection in graphs for applications like diffusion dynamics and opinion dynamics, but it is incremental as it builds on existing spectral methods with a new modeling framework.
The paper tackles the problem of detecting communities in a graph from observed signals modeled as noisy outputs of an unknown graph filter excited by low-rank inputs, and shows that applying a spectral method to the covariance matrix can effectively retrieve the community structure, with performance depending on a low-pass property of the filter.
This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on a `low-pass' property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical experiments demonstrate that our approach is effective.