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Dynamic networks consist of a sequence of time-varying networks, and it is ofgreat importance to detect the network change points. Most existing methodsfocus on detecting abrupt change points, necessitating the assumption that theunderlying network probability matrix remains constant between adjacent changepoints. This paper introduces a new model that allows the network probabilitymatrix 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 subspacechange points, followed by a carefully refined detection procedure.Theoretically, we show that the proposed method is asymptotically consistent interms of change point detection, and also establish the impossibility regionfor detecting these network subspace change points. The advantage of theproposed method is also supported by extensive numerical experiments on bothsynthetic networks and a UK politician social network.

Change point detection in dynamic heterogeneous networks via subspace tracking