International Linear Algebra Society Conference edition:20 location:Leuven, Belgium date:July 11-15, 2016
In applications, one rarely works with tensors that admit an exact low-rank tensor decomposition due to the occurrence of various sources of error, such as sampling, measurement, approximation, modeling, and roundoff. This implies that one often attempts to recover the true decomposition from the noisy tensor.
Several applications, such as fluorescence spectroscopy, crucially depend on the uniqueness of the tensor rank decomposition for interpreting the individual rank-1 tensors appearing in the decomposition. Hitherto it has been poorly recognized that one is trying to interpret the rank-1 terms of the true decomposition, which are assumed to be unique, based on the rank-1 terms appearing in the approximate decomposition while there is no a priori reason to assume that the distance between these two sets of rank-1 terms is small, even when the approximate tensor is a very good approximation to the true tensor.
In this talk, I will present the first upper bound that allows one to bound the perturbation error to the individual rank-1 terms based only on knowledge of the perturbation to the tensor.