Identification of Kernel Regression Model Using Double Norms Method

Abstract

Considering that conventional nonlinear dynamic system modeling approaches from a finite set of measured data is not prone to control the model structure complexity, and those methods can also lead to over-fitting problems, a new method based on double norms is proposed to identify kernel regression model which is guaranteed by identifying accuracy and model sparsity . From the point of view of dominating the model structure complexity and improving the identification accuracy, the proposed method combines L 1 -norm structural risk minimization theory with some ideas from L ∞ -norm on approximation error minimization to construct the optimization problem of kernel regression model. Following that, the optimization can be solved by the simpler linear programming. The method has the following remarkable features: 1) identifying accuracy can be guaranteed by the L 1 -norm minimization on approximation error; 2)model structural complexity is under control by introducing L 1 -norm on structural risk within the framework of support vector regression (SVR) to guarantee the model sparsity; 3)the optimality of the proposed method adopts the equilibrium between the identifying accuracy and sparseness. Finally, rationalities and superiorities of the proposed method in identifying nonlinear dynamic system is demonstrated by experiments.