A survey of tensor methods

Matrix decompositions have always been at the heart of signal, circuit and system theory. In particular, the singular value decomposition (SVD) has been an important tool. There is currently a shift of paradigm in the algebraic foundations of these fields. Quite recently, nonnegative matrix factorization (NMF) has been shown to outperform SVD at a number of tasks. Increasing research efforts are spent on the study and application of decompositions of higher-order tensors or multi-way arrays. This paper is a partial survey on tensor generalizations of the SVD and their applications. We also touch on nonnegative tensor factorizations.