Tensor decompositions and their sensitivity

The tensor rank decomposition or CPD expresses a tensor as a minimum-length linear combination of elementary rank-1 tensors. It has found application in fields as diverse as psychometrics, chemometrics, signal processing and machine learning, mainly for data analysis purposes. In these applications, the theoretical model is oftentimes a low-rank CPD and the elementary rank-1 tensors are usually the quantity of interest. However, in practice, this mathematical model is always corrupted by measurement errors. In this talk, we will investigate the numerical sensitivity of the CPD using techniques from algebraic and differential geometry.