Title: Towards a perturbation theory for the tensor rank decomposition
Authors: Vannieuwenhoven, Nick
Issue Date: 4-Jun-2015
Conference: Seminari di analisi numerica location:Pisa, Italy date:June 4, 2015
Abstract: The tensor rank decomposition is a decomposition of a tensor into a linear combination of rank-1 tensors. One of the key advantages of higher-order tensors is that this decomposition is generally unique, which allows for an interpretation of the individual rank-1 terms. Because of this property, the tensor rank decomposition has found application in several domains. For instance, they can be used as a clustering algorithm in an unsupervised learning setting assuming a certain statistical model wherein each of the rank-1 tensors in the decomposition will correspond with a cluster. In the applications where tensor rank decompositions arise, the tensor is usually known only up to some small perturbation error. This raises the following interesting problem: Suppose that the tensor is perturbed by a small quantity, by how much can the individual rank-1 terms change relative to the magnitude of the perturbation? Can it be unbounded? In this presentation, I will explore the definition of a possible condition number that answers these questions up to first order.
Publication status: published
KU Leuven publication type: AMa
Appears in Collections:Numerical Analysis and Applied Mathematics Section

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