Feature selection for nonlinear stochastic system classification

A decision-theoretic formulation is given for the problem of classifying an unknown nonlinear stochastic system into one of M classes when only input-output measurements are available. This leads directly to a pattern recognition solution for the problem, and Bayes-risk theory yields the likelihood-ratio test for class determinations. Parameterizations which yield an implicit description for unknown nonlinear systems are considered, and the theoretical likelihood ratio is related to these parameterizations. The difficult problem of initial feature selection is considered in terms of a parameter vector, and in terms of a quasi-moment expansion, both of which require no a priori knowledge of the system. Experimental results are also cited which show that classification can be accomplished with a low probability of error, and analogies with other classification problems are noted.