Change point detection in dynamic heterogeneous networks via subspace tracking

Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the underlying network probability matrix remains constant between adjacent change points. This paper introduces a new model that allows the network probability matrix to undergo continuous shifting, while the latent network structure, represented via the embedding subspace, only changes at certain time points. Two novel statistics are proposed to jointly detect these network subspace change points, followed by a carefully refined detection procedure. Theoretically, we show that the proposed method is asymptotically consistent in terms of change point detection, and also establish the impossibility region for detecting these network subspace change points. The advantage of the proposed method is also supported by extensive numerical experiments on both synthetic networks and a UK politician social network.