ON SHAPE OF PATTERN ERROR FUNCTION, INITIALIZATIONS AND INTRINSIC DIMENSIONALITY IN ANN CLASSIFIER DESIGN

'. J;\.bstract. An analytical equation for a generalization error of minimum empirical error classifier is derived for a case when true classes are spherically Gausslan. It is compared with the generalization error of a mean squared error classifier a standard Fisher linear discriminant function. In a case of.spherically distributed classes the generalization error depends on a distance between the classes and a number of training samples. It depends on an intrinsic dimensionality of a data only via initialization of a weight vector. If initialization is sU,ccessful the dimensionality does not effect the generalization error. It is concluded advantageous conditions to use artificial neural nets are to classify patterns in a changing environment, when intrinsic dimensionality of the data is low or when the number of training sample vectors is really large. !