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

机译：基于核的系统识别的流形正则化方法比较

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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 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.
机译：在本文中，我们提供了一个仿真研究，以研究流形正则化在基于核的非参数非线性SISO（单输入单输出）系统识别方法中的作用。解决此问题的方法是估计静态非线性函数，该函数将回归变量（包含动态系统输入和输出的过去值）映射到系统输出。与Tikhonov方法相反，歧管正则化对估计函数强制执行局部平滑约束。它基于以下假设：回归变量位于回归变量空间中的流形上。通常用连接回归变量的加权图来近似该流形。当为图形连接及其权重做出不同选择时，本工作将分析基于内核的方法估计的性能。该方法已在基准非线性系统模型上针对不同的连接和权重策略进行了测试。结果给出了最有前途的选择的直觉，以便采用流形正则化进行系统识别。

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