Clustering of heterogeneous populations of networks

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might be different on weekdays and weekends, for instance. Brain networks may differ between healthy patients and those with dementia or other conditions. Here we describe a Bayesian analysis framework for such data that allows for the fact that network measurements may be reflective of multiple possible structures. We define a finite mixture model of the measurement process and derive a Gibbs sampling procedure that samples exactly from the full posterior distribution of model parameters. The end result is a clustering of the measured networks into groups with similar structure. We demonstrate the method on both real and synthetic network populations.