Abstract

Tensors, or multiindexed arrays, play an important role in fields such as machine learning and signal processing. These higher-order generalizations of matrices allow for preservation of higher-order structure present in data, and low rank decompositions of tensors allow for recovery of underlying information. One of the most popular decompositions for tensors is the canonical polyadic decomposition (CPD) which expresses a tensor as a sum of rank one tensors. However most existing algebraic algorithms for CPD (based on generalized eigenvalue decomposition) are unstable. In this talk, I will present a new algebraic algorithm which significantly improves the accuracy for tensor decompositions. In addition, I will discuss progress on some fundamental issues related to tensor decompositions.

Biography

I am a postdoctoral researcher at KU Leuven working in the group of Lieven de Lathauwer. I received my PhD from UC San Diego in 2018 under the direction of J. William Helton. My primary research interests include tensor decompositions and noncommutative (matrix) convex sets. In the tensors world, I study existence of best low rank tensor approximations and algebraic algorithms for various tensor decompositions. For matrix convex sets, I am particularly interested in various types of extreme points.