Dimensionality Reduction of Volterra Kernels by Tensor Decomposition using Higher-Order SVD

Dimensionality Reduction of Volterra Kernels by Tensor Decomposition using Higher-Order SVD

Title : Dimensionality Reduction of Volterra Kernels by Tensor Decomposition using Higher-Order SVD
Authors :
Baras, John S.
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.

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