Cumulant tensors

Cumulants of multidimensional random variables satisfy the properties that allow them to be considered as tensors. Most cumulant-based signal processing algorithms actually use slices of those tensors, mainly because numerical algorithms available today are only able to manipulate matrices. In addition, very few works in the literature have addressed the problem of decomposing or factorizing tensors. This would be a discrepancy if the problem was not so difficult, as emphasized in the talk. However, it is still possible to establish some links with the Eigenvalue decomposition, the congruent diagonalization, or the Cholesky factorization of matrices. But striking differences can be pointed out. It is hoped that these first basic statements will motivate further developments of tensor-based algorithms.