III: Small: Explaining heterogeneity within and across evolving networks

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This project will develop novel methods for analyzing and modeling heterogeneous dynamic networked data. Network data arises in a number of application domains ranging from Internet of Things, cloud computing, software analysis, neuroscience, biology, geography, to social sciences. Accordingly, network analysis has emerged as a major paradigm for exploring complex processes behind observed data. Compared to high dimensional data, analysis of network data is more challenging due to interdependencies between entities, the presence of attributes, and the natural evolution of networks over time. The goal of the project will be to understand and model the heterogeneity of behaviors in dynamic networks. The project will have a transformative impact on big data problems that are enabled by a network-centric approach to exploiting dynamic, heterogeneous data, such as brain networks. The project will integrate research and education by introducing methods and results of the project into courses and seminars, and train a diverse group of undergraduate and graduate students.The project's focus will be on heterogeneity in dynamic networks: heterogeneity of node behaviors across network structure and time, heterogeneity of the coupling of structure and attributes, and heterogeneity across networks. Against this backdrop, the project will consider the basic problems of clustering (partitioning), classification/regression, decomposition of networks into its basis elements, and the problem of explaining global network behaviors by small network fragments. These problems will be considered for a single network and for multiple networks. Within a network, heterogeneity is observed when nodes or clusters exhibit different behaviors, for instance due to hidden or missing data. Across networks, heterogeneity is observed in the diversity of subject populations or among network instances. The first research thrust will apply spectral theory for partitioning attributed and dynamic networks. The second research thrust will apply convex optimization to find clusters while tolerating heterogeneity across network structure and time. It will also develop methods for estimating graphical models for multiple dynamic networks. The final research thrust will focus on the discovery of succinct sub-networks that are predictive and that evolve concurrently with the underlying networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.