Hibernating Process: Modelling Mobile Calls at Multiple Scales

Do mobile phone calls at larger granularities behave in the same pattern as in smaller ones? How can we forecast the distribution of a whole month´s phone calls with only one day´s observation? There are many models developed to interpret large scale social graphs. However, all of the existing models focus on graph at one time scale. Many dynamical behaviors were either ignored, or handled at one scale. In particular new users might join or current users quit social networks at any time. In this paper, we propose HiP, a novel model to capture longitudinal behaviors in modeling degree distribution of evolving social graphs. We analyze a large scale phone call dataset using HiP, and compare with several previous models in literature. Our model is able to fit phone call distribution at multiple scales with 30% to 75% improvement over the best existing method on each scale.