  We consider the detection and localization of change points in the
distribution of an offline sequence of observations. Based on a nonparametric
framework that uses a similarity graph among observations, we propose new test
statistics when at most one change point occurs and generalize them to multiple
change points settings. The proposed statistics leverage edge weight
information in the graphs, exhibiting substantial improvements in testing power
and localization accuracy in simulations. We derive the null limiting
distribution, provide accurate analytic approximations to control type I error,
and establish theoretical guarantees on the power consistency under contiguous
alternatives for the one change point setting, as well as the minimax
localization rate. In the multiple change points setting, the asymptotic
correctness of the number and location of change points are also guaranteed.
The methods are illustrated on the MIT proximity network data.
