Tensor approximation by block term decomposition

Details

Supervisors

Absil, Pierre-Antoine ; De Lathauwer, Lieven

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées

Abstract

Higher-order tensors have become a powerful tool in many areas of applied mathematics such as statistics or scientific computing. They also have found many applications in signal processing and machine learning. As suggested by the literature, higher-order tensors draw their power notably from the many tensor decompositions among which the block term decomposition holds a central place. The purpose of this master's thesis is to focus on the computation of the best approximation in the least-squares sense of a given third-order tensor by a block term decomposition. Using variable projection, the tensor approximation problem is expressed as a minimization of a cost function on a product of Stiefel manifolds. In this master's thesis, I apply two first-order algorithms from the framework of optimization on matrix manifolds to minimize this cost function. I investigate the performance of these two new methods and compare them with the already available ones