Program

Part I: Signal Processing [M. Vetterli et al., “Foundations of Signal Processing”]

Definition of signals, signal properties, discrete representations, Fourier transforms, filtering, sampling theory, applications to audio signals and images

Sparse representations, compressive sensing

Part II: Processing over graphs [M.E.J. Newman, “Networks: An Introduction”; S. Barbarossa, “Signal Processing over Graphs”]

Algebraic graph theory, graph properties, connectivity

Graph features: degree centrality, eigenvector centrality, PageRank, betweeness, modularity

Graph models: random graphs, random geometric graphs, small worlds graphs, scale-free graphs

Independence graphs: Markov networks, Bayes networks, Gaussian Markov Random Fields

Operations on graphs: partitioning

Signals defined on graphs

Filtering and sampling signals over graphs

Prediction of processes over graphs

Inference of graph topology from data

Part III: Distributed optimization over networks [S. Boyd et al. “Distributed Optimization and Statistical    

                                                                                 Learning via the Alternating Direction Method of Multipliers”]

Convex optimization

Primal and dual decomposition

Alternating direction method of multipliers

Algorithms for sparsity constrained problems

Consensus problems

Sharing problems

Part IV: Examples of application

Graph-based methods for machine learning

Graph topology inference from data (brain, finance, ...)

Matrix completion