Least Squares Support Vector Machines for Kernel CCA in Nonlinear State-Space Identification

We show that kernel canonical correlation analysis (KCCA) can be used to construct a state sequence of an unknown nonlinear dynamical system from delay vectors of inputs and outputs. In KCCA a feature map transforms the available data into a high dimensional feature space, where classical CCA is applied to find linear relations. The feature map is only implicitly defined through the choice of a kernel function. Using a least squares support vector machine (LS-SVM) approach an appropriate form of regularization can be incorporated within KCCA. The state sequence constructed by KCCA can be used together with input and output data to identify a nonlinear state-space model. The presented identification method can be regarded as a nonlinear extension of the intersection based subspace identification method for linear time-invariant systems.