The next talk of the Idiap Speaker Series will take place at Idiap on July the 20th, 11H00, conference room 106.

The Prof. Bart Vandereycken from the University of Geneva will give the talk entitled: Algorithms on manifolds: geometric means and recommender systems.

Abstract: Many data in scientific computing and machine learning is highly structured. When this structure is given as a mathematically smooth manifold, it is usually advisable to explcilty exploit this property in theoretical analyses and numerical algorithms. I will illustrate this using two examples. In the first, the manifold is classical: the set of symmetric and positive definite matrices. The problem we consider is the computation of the geometric mean, also called Karcher mean, which is a generalization of the arithmetic mean where we explicitly take into account that the data lives on a manifold. The application is denoising or interpolation of covariance matrices. The other example considers a non-standard manifold: the set of matrices of fixed rank. The application is now recommender systems (the Netflix problem) and the algorithm low-rank matrix completion. I will show that one of the benefits of the manifold approach is that the generalisation to low-rank tensor completion is conceptually straightforward but also computationally efficient.

Previous Idiap Speaker Series (webcast) can be found here: Idiap talks