A new Algorithm for Overcomplete Tensor Decomposition based on Sums-of-Squares Optimisation

Abstract

In this thesis, a new class of algorithms based on Sums of Squares Programming is developed. These allow to reduce a degree-$d$ homogeneous polynomial $T={\sum }_{i=1}^m⟨a_i,X{⟩}^d$ to a quadratic form being close to a rank-$1$ form via a low-degree reduction polynomial $W\in \sum \mathbb{R}[X{]}^2$. $W$ can be thought of as a `weight function' attaining high values on merely one of the components $a_i$. The component can then be extracted by running an eigenvalue decomposition on the quadratic form ${\sum }_{i=1}^{m}W(a_i)⟨a_i,X{⟩}^2$.

~70 pages. Master's Thesis being uploaded for reference

References in corpus (1)

• Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms