Parametric complexity reduction of Volterra models using tensor decompositions

Discrete-time Volterra models play an important role in many application areas. The main drawback of these models is their parametric complexity due to the huge number of their parameters, the kernel coefficients. Using the symmetry property of the Volterra kernels, these ones can be viewed as symmetric tensors. In this paper, we apply tensor decompositions (PARAFAC and HOSVD) for reducing the kernel parametric complexity. Using the PARAFAC decomposition, we also show that Volterra models can be viewed as Wiener models in parallel. Simulation results illustrate the effectiveness of tensor decompositions for reducing the parametric complexity of cubic Volterra models.