Blind Community Detection from Low-rank Excitations of a Graph Filter

This paper considers a novel 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 low-rank inputs. Rather than learning the precise parameters of the graph itself, the proposed method retrieves the community structure directly; Furthermore, as in blind system identification methods, it does not require knowledge of the system excitation. The paper shows that communities can be detected by applying spectral clustering to the low-rank output covariance matrix obtained from the graph signals. The performance analysis indicates that the community detection accuracy depends on the spectral properties of the graph filter considered. Furthermore, we show that the accuracy can be improved via a low-rank matrix decomposition method when the excitation signals are known. Numerical experiments demonstrate that our approach is effective for analyzing network data from diffusion, consumers, and social dynamics.