Randomly Generated Nonlinear Transformations for Pattern Recognition

In many mathematical and engineering problems the solution is simpler after a transformation has been applied. A general method is proposed to find suitable transformations for discrete data in information processing problems. The main feature of the method is random perturbation of the data subject to constraints which ensure that, in the transformed space, the problem is in some sense simpler and that the local structure of the data is preserved. An application of this technique to pattern recognition is discussed where a transformation is found for the feature space such that classes, which are not linearly separable in the original space, become so in the transformed space. The transformation considerably simplifies the problem and allows well-developed linear discriminant techniques to be applied. This application was implemented and tested with a number of examples which are described.