Midterm colloquium Nico Verbeek

Title: A kernelizable primal-dual formulation of the Multi-Linear Singular Value Decomposition.

Supervisor: Dr.Ir. Kim Batselier

Abstract: Multilinear Singular Value Decomposition (MLSVD) is a widely used linear decomposition method for higher-order tensors, with applications in machine learning and signal processing.  Traditionally, MLSVD is computed by solving a set of linear equations under specific constraints. However, recent research has found a way to reformulate MLSVD into a primal-dual optimization framework, of which the dual corresponds to the classical MLSVD. This new formulation enables a non-linear extension of MLSVD (KMLSVD) opening doors for advanced and possibly unexplored applications in machine learning, such as self-attention mechanisms on 3D tensor data. However, despite its potential, solving the primal MLSVD formulation remains an open challenge. Successfully resolving this challenge would enable a deeper look into the validity of primal-dual KMLSVD applications.