Title: Understanding Tensor and Tensor Decompositions

Abstract: Tensors are multidimensional arrays that can play a key role in the representation of big data. Decompositions of higher-order tensors have applications in biochemistry, signal processing, data mining, neuroscience, and elsewhere. The talk will present commonly used tensor operations and different types of tensor decomposition. Specifically, it will illustrate the CANDECOMP/PARAFAC (CP) decomposition and the Tucker decomposition, which are examples of decompositions that have been employed to optimize the storage of large high-order tensors that arise naturally in different scientific fields. Computation with the decomposed tensors, however, is still an actively growing field of research that promises to offer new insights into solving classic problems in numerical analysis.