Fuchs, Jean Jacques (Univ. de Rennes 1)

Towards a New Matrix Decomposition

Scheduled for presentation during the Regular Session "Optimization" (TuP12), Tuesday, July 25, 2006, 16:10−16:35, Room 104b

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

Low rank matrix approximations have many applications in different domains. In system theory it has been used in model reduction schemes, in system identification with output-error models and in static errors-in-variables problems, for instance. The approximations are mostly performed using the singular value decomposition. This is optimal for all unitarily invariant matrix norms, such as the Frobenius norm. From a statistical point of view it is justified when the components are perturbed by independent and identically distributed zero mean Gaussian noise. If this assumption is

not valid other norms and thus approximations should be considered. Below we consider the l1-norm that is optimal if the noise samples follow the Laplace or double-exponential distribution and we indicate how to obtain for an arbitrary

matrix, the optimal decomposition -similar to the singular value decomposition- associated with this norm.