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In this paper we explore the potential of using a general class of functional representation techniques, kernel-based regression, in the nonlinear model reduction problem. The kernel-based viewpoint provides a convenient computational framework for regression, unifying and extending the previously proposed polynomial and piecewise-linear reduction methods. Furthermore, as many familiar methods for linear system manipulation can be leveraged in a nonlinear context, kernels provide insight into how new, more powerful, nonlinear modeling strategies can be constructed. We present an SVD-like technique for automatic compression of nonlinear models that allows systematic identification of model redundancies and rigorous control of approximation error.