Mathematical model of the integral classification criterion and the algorithm for forming its graphical representation

Background. The most important method of scientific research is classification. The task of classifying objects with a heterogeneous space of information features, which currently has no unified solution, is particularly difficult. It is important to take into account the dependence of classification results on chosen point of view on subject area – a criterion that determines composition and typology of significant features of objects under consideration. The purpose of the work is the mathematical and algorithmic formalization of the process of developing classification criteria, as well as development of a unified format for presenting information features of an object regardless of their type, composition and completeness. This will reduce classification task to a single automated process - well-managed, visual, amenable to machine learning and invariant to specifics of subject area. Materials and methods. The work reveals the main problems of traditional approaches to solving the classification problem, in context of dynamic points of view on subject area. Existing works devoted to formalization of classification criteria and problems of choosing significant information features of objects are considered. The methodological basis of the work is set theory, machine learning methods, neural networks and raster computer graphics. Results. As a result, a concept and formalized set-theoretic representation of the integral classification criterion are proposed. The criterion allows algorithmization of choice of view’s points on the studied subject area. Classification criteria determine composition of significant features of the object. For its unified representation, a single format in the form of a raster graphic image - a graphic-chromatic map, as well as an algorithm for creation of such maps have been developed. Conclusions. The proposed approach significantly simplifies the procedure of distributing heterogeneous objects into classes by reducing it to a well-studied and proven task of machine learning - classification of raster graphic images. Formalization of the integral classification criterion allows quickly and conveniently set different points of view on the subject area, representing them in the form of data tuples. The algorithm for forming grapho-chromatic maps provides obtaining raster images of a single size and format for feeding to the input of a pretrained neural network classifier. At the same time, when changing the point of view on the subject area (i.e. when changing the number and composition of significant features of objects), there is no need to change the structure of the classifier or retrain it.