Tensor decompositions such as the tensor rank decomposition (CPD), block-term decomposition, or (partially) symmetric tensor rank decomposition express a tensor as a linear combination of elementary tensors. They find application in chemometrics, computer science, machine learning, psychometrics, and signal processing. Their uniqueness properties render them suitable for data analysis tasks in which the elementary tensors are the quantities of interest. However, in applications, this idealized mathematical model is always corrupted by measurement errors. For a robust interpretation of the data, it is therefore imperative to quantify how sensitive these elementary tensors are to perturbations of the whole tensor. In this talk, I will give an overview of recent results on the sensitivity of such tensor decompositions established with my collaborators Carlos Beltran, Paul Breiding, and Nick Dewaele.
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