Associate Professor (Reader) in Machine Learning
School of Mathematics, The University of Edinburgh
The Maxwell Institute for Mathematical Sciences
Alan Turing Institute | Bayes Centre | Gen AI Lab
School of Mathematics, Gran Sasso Science Institute
email: f dot tudisco at ed.ac.uk
Last day of the first virtual SIAM Imaging Science conference today. I am presenting a talk at the minisymposium Nonlinear Spectral Analysis with Applications in Imaging and Data Science organized by Leon Bungert (Friedrich-Alexander Universitaet Erlangen-Nuernberg, Germany), Guy Gilboa (Technion Israel Institute of Technology, Israel) and Ido Cohen (Israel Institute of Technology, Israel).
These are title and abstract of my talk:
Nodal Domain Theorem for the p-Laplacian on Graphs and the Related Multiway Cheeger Inequality
We consider the p-Laplacian on discrete graphs, a nonlinear operator that generalizes the standard graph Laplacian (obtained for p=2). We consider a set of variational eigenvalues of this operator and analyze the nodal domain count of the corresponding eigenfunctions. In particular, we show that the famous Courant’s nodal domain theorem for the linear Laplacian carries over almost unchanged to the nonlinear case. Moreover, we use the nodal domains to prove a higher-order Cheeger inequality that relates the k-way graph cut to the k-th variational eigenvalue of the p-Laplacian.
Below you can find my slides, in case you wish to have a look at them