  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.
