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
I am very excited I will be giving a minitutorial on Applied Nonlinear Perron–Frobenius Theory at the SIAM conference on Applied Linear Algebra (LA21).
I will present the tutorial together with Antoine Gautier.
We will introduce the concept of multihomogeneous operators and we will present the state-of-the-art version of the nonlinear Perron-Frobenius theorem for nonnegative nonlinear mappings. We will discuss several numerical optimization implications connected to nonlinear and higher-order versions of the Power and the Sinkhorn methods and several open challenges, both from the theoretical and the computational viewpoints. We will also discuss numerous problems in data mining, machine learning and network science which can be cast in terms of nonlinear eigenvalue problems with eigenvector nonlinearities and we will show how the nonlinear Perron-Frobenius theory can help solve them.