Gradient-based approaches to learn tensor products

Tensor algebra has become of high interest recently due to its application in the field of so-called Big Data. For signal processing a first important step is to compress a vast amount of data into a small enough set so that particular issues of interest can be investigated with todays computer methods. We propose various gradient-based methods to decompose tensors of matrix products as they appear in structured multiple-input multiple-output systems. While some methods work directly on the observed tensor, others use input-output observations to conclude to the desired decomposition. Although the algorithms are nonlinear in nature, they are being treated as linear estimators; numerical examples validate our results.