Construction of decision rules for pattern recognition in the event of erroneous division of classes of the training sample.

The article considers the solution of the problem of pattern recognition with a given error and reliability, when the classes of the training sample are separated from each other with an error in the feature space, the dimension of which has an upper limit value. A method is presented for finding the upper bound on the size of the feature space, taking into account such parameters as the frequency of errors in the erroneous separation of each class of the training sample from other classes, the probability of error in recognition and its reliability, as well as the number of classes, features and objects in the training sample. In order to form a finite-dimensional space from individual class-specific features, the minimum and real separating strength of each selected individual feature is determined. Procedures for the formation of a finite-dimensional space from each type of individual features of the second and third types are proposed, taking into account their minimum and real separating forces. Based on the proposed methodology, an algorithm and software were developed. Computational experiments were carried out on a computer, and the results were presented in the form of decision rules, according to which new images were recognized. The conclusions of the study are also presented. [ABSTRACT FROM AUTHOR]