Data-Driven Discovery of Linear Dynamical Systems Over Graphs via Dynamical Sampling
Explore data-driven discovery of linear dynamical systems over graphs through dynamical sampling in this lecture from the Focus Program on Analytic Function Spaces and their Applications. Delve into graph signal processing, examining how to recover missing information on graph nodes efficiently and robustly. Investigate preliminaries of graph signal sampling, its relation to frame/basis theory in harmonic analysis, and previous work on deterministic dynamical sampling. Learn about space-time sampling formulation and three proposed random space-time sampling regimes. Discover optimal sampling distributions based on graph structure and reconstruction strategy. Examine guarantees for standard and efficient decoders, system identification in dynamical sampling, and generalizations to affine systems. Conclude with numerical results demonstrating the effectiveness of the presented methods.