Whenever network scientists work with real-world diffusion data -attempting for instance to analyse the spreading an opinion in a social network or to identify the source of a rumor- they have to face a common challenge: to interpret complex network-level behavior on the basis of the network connectivity.
One of the mathematical tools suitable for the analysis of data supported over networks is the graph Fourier transform (GFT), a tool which has recently gained significant attention . Nevertheless, despite its good mathematical properties, GFT often falls short in the analysis of real data, especially when diffusion processes are concerned.
This project aims to understand, using tools from graph theory and matrix theory, why GFT falls short in the analysis of real diffusion processes, as well as to find ways of circumventing the problem. For this to be successful, two components are necessary: a strong mathematical framework and experimentation with real data.
What you are going to learn: systems modeling, spectral graph theory, convex optimization.
What you should know: linear algebra, basic graph theory, MATLAB.
Theory: 3/5 Application: 2/5
Interested? Contact Andreas Loukas (email@example.com) for more details.
 The Emerging Field of Signal Processing on Graphs, David I Shuman, Sunil K. Narang, Pascal Frossard, Antonio Ortega, and Pierre Vandergheynst, 2013