PhD comprehensive seminar | Alex Howse, Iterative and Multilevel Optimization Methods: the Tucker Tensor Decomposition Problem and Beyond

Iterative and Multilevel Optimization Methods: the Tucker Tensor Decomposition Problem and Beyond

A tensor is a multidimensional array. The Tucker tensor decomposition is a way of representing a tensor as the product of a tensor and a set of matrices. The Tucker decomposition has applications in such areas as image classification, chemical analysis, and multi-way statistical analysis. Furthermore, by restricting the ranks of these matrices, we can create an approximation of this tensor with much lower storage costs.

In this talk we will briefly consider the methods of matrix manifold optimization, the alternating direction method of multipliers, and multilevel optimization, with a particular focus on how these methods may be used in the context of the Tucker tensor approximation and similar problems.