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

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