  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.
