Higher-order tensors are the natural generalization of vectors (first order) and matrices (second order). They are becoming increasingly important in signal processing, data mining, scientific computing and many other fields. One reason for this is the fact that tensor decompositions are often unique under mild assumptions, while their matrix counterparts are only unique under quite restrictive conditions. This makes tensors natural tools for data interpretation. In practical applications, tensor decompositions are usually fitted to the data at hand, the misfit resulting from noise or model mismatch. The optimization can be challenging, for instance because it amounts to a search over a set that is not closed. On the other hand, tensor decompositions can also be used as compact representations of quantities of interest, and as such allow a significant speed-up of scientific computations, for instance in the context of optimization in high dimensions.
The goal of this SIG is to further develop the tensor toolkit and study promising applications.
Links with Working Groups:
WG2: modelling problems with high dimensionality and large data sets
WG5: large-scale matrix equations and inequalities
Coordinator: Lieven De Lathauwer
Members: Lieven De Lathauwer, Ignat Domanov, Laurent Sorber, Mikael Sorensen, Marc Van Barel, Raf Vandebril
