Dimensionality Reduction of Volterra Kernels by Tensor Decomposition using Higher-Order SVD
Authors :
Libal, Urszula
Johansson, Karl Henrik
Conference : 2020 59th IEEE Conference on Decision and Control (CDC) pp. 5935-5941
Date: December 14 - December 18, 2020
The paper proposes a practical method for a significant dimensionality reduction of Volterra kernels, defining a discrete nonlinear model of a signal by Volterra series of higher order. In system identification of Volterra series, the Volterra kernels and nonlinear inputs of the system can be described by super-symmetrical tensors. The reduction of their dimensionality is obtained by a tensor decomposition technique called Higher Order Singular Value Decomposition (HOSVD). The main contribution of the paper is a cascade learning algorithm for the system identification based on residuals of least squares minimization. Numerical examples for Volterra system of order four are used to illustrate the approach.
Download Full Paper