A comparison of manifold regularization approaches for kernel-based system identification

M. Mazzoleni, M. Scandella, F. Previdi

In this paper, we present a simulation study to investigate the role of manifold
regularization in kernel-based approaches for nonparametric nonlinear SISO (Single-Input
Single-Output) system identification. This problem is tackled as the estimation of a static
nonlinear function that maps regressors (that could contain past values of both input and
output of the dynamic system) to the system outputs. Manifold regularization, as opposite to the
Tikhonov one, enforces a local smoothing constraint on the estimated function. It is based on the
assumption that the regressors lie on a manifold in the regressors space. This manifold is usually
approximated with a weighted graph that connects the regressors. The present work analyzes
the performance of kernel-based methods estimates when different choices are made for the
graph connections and their respective weights. The approach is tested on benchmark nonlinear
systems models, for different connections and weights strategies. Results give an intuition about
the most promising choices in order to adopt manifold regularization for system identification.