B1070
Title: Exploratory data analysis for dynamic networks
Authors: Paromita Dubey - University of Southern California (United States) [presenting]
Abstract: Samples of dynamic or time-varying networks are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data analysis are infeasible when observations are time courses of networks or other complex non-Euclidean random objects that are elements of general metric spaces. We combat this complexity by a generalized notion of mean trajectory taking values in the object space. For this, we adopt pointwise Frechet means and then construct pointwise distance trajectories between the individual time courses and the estimated Frechet mean trajectory, thus representing the time-varying objects and networks by functional data. Functional principal component analysis of these distance trajectories can reveal interesting features of dynamic networks and object time courses and is useful for downstream analysis. The approach also makes it possible to study the empirical dynamics of time-varying networks, including dynamic regression to the mean or explosive behavior over time. We demonstrate desirable asymptotic properties of sample-based estimators for suitable population targets under mild assumptions. The utility of the proposed methodology is illustrated with Chicago Divvy Bike networks.
