Localizing Sources of Network Diffusion via Graph Signal Processing

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Localizing Sources of Network Diffusion via Graph Signal Processing Over the past decade there has been a growing fascination with the complex connectedness of modern society. As a result of the pervasive interest in scientific analysis at a system level along with the ever-growing capabilities for high-throughput data collection in various fields, the study of networks has increased dramatically with multidisciplinary research efforts from researchers ranging from physics to systems engineering and the bio-behavioral sciences. As modern interconnected systems grow in size and importance, while they become more complex and heterogeneous, there is an urgent need to advance a holistic theory of networks. In this context, research in this project will contribute towards understanding the inherent complexities of large-scale and strongly coupled systems ranging from critical engineering infrastructures to the brain. It will also impact teaching and design of networks, as well as signal processing theory and practice at the fundamental level. At a broader scale, through cross-domain extrapolation of this project's Network Science leitmotif, the insights and technologies developed here will provide valuable tools for fundamental science and engineering research, positively impact environment and economy, and permeate benefits to cyber-security, IoT technologies, neuroscience, healthcare and sensing-integration for cyber-physical systems.This research effort places particular emphasis on modeling, identification, and controllability of distributed network processes - often conceptualized as signals defined on the vertices of a graph. To untangle the latent structure of such signals, the key novel insight is to view them as outputs of unobserved graph filters that model the emergence of complex network dynamics. Albeit simple, graph filters are appealing since they represent linear transformations between graph signals that can be implemented via local interactions among nodes, and they are well-suited to model network diffusion processes while remaining analytically tractable. In this direction, the research agenda is to develop novel theory and algorithms for the challenging problem of localizing sources of network diffusion given an observed (output) graph signal, e.g., a spatial temperature profile measured by a wireless sensor network, an opinion profile in a social network, or the neural activity in different regions of the brain. At a fundamental level, this effort broadens the scope of classical blind system identification to networks, or, of blind deconvolution of temporal and spatial signals to unstructured graph domains. Advocating a graph signal processing approach the aim tis o boost the interest in the area beyond its theoretical aesthetics as an elegant generalization of classical signal processing, and highlight its practical implications when solving real-world engineering problems encountered with sensor, social and brain networks, to name a few.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.