Principal component analysis in nonlinear systems: Preliminary results

Abstract

Principal component analysis (Hotelling, 1933), supported by the "state of the art" algorithm (Golub and Reinsch, 1970) for performing singular valud decomposition, is a powerful tool which has been applied (Moore, 1979) successfully in the analysis of linear systems. In this paper attention is called to the fact that it is also a very useful tool for computing and evaluating affine approximations of multi-dimensional nonlinear maps over specified domains. Included are preliminary ideas about application of the tool to the following problems: numerical linearization of dynamic systems, gradient approximations for optimization, and numerical differentiation of vector time signals.