Integer-valued problems of transforming the training tables in k-valued code in pattern recognition problems

Abstract In this paper the integer-valued problems of transforming the descriptions of training objects represented in the training tables through an arbitrary code into a k-valued code are formulated. From the condition that the classes are non-intersecting, it follows that the minimum k-valued coding exists. The problems defined are of the type of integer-valued systems of equations and inequalities, as well as of the type of integer-valued optimization problems. Effective algorithms for solving these problems are suggested.