Resumen
The article discusses the application of data mining methods in the educational process. The possibilities of their implementation in the training process as functional tools of training information systems are analyzed. Features of their use to build optimal learning paths of students are considered. Galois's compliance methodology is proposed as a method of data mining in such systems. The author describes versions of its application in case of representation of the subject area in the form of a graph model G of educational material. On the examples of graph models, various possible situations are characterized. Case classification is based on the allocation of sets of non-learned knowledge elements associated with the vertices of graph G. Parameters of diameter d and number of vertices are selected as criteria of division into subsets. For each of the cases d = 0, d = 1 and d = 2 a meaningful interpretation is given. The case with n vertices of diameter d of more than two is also disassembled. Based on the identified situations, a rule is formulated for the subgraphs G1, G2, ..., Gn of the graph G according to unlearned knowledge elements for each student. This allowed to describe the algorithm of application of Galois correspondence as a method of data mining in training information systems. The author consistently gives a characteristic of each of the stages of the algorithm. Particular importance is attached to the formation of optimal training strategies in accordance with the identified cases of application of the Galois methodology for the graph model G of the material under study. The relevance of the article is related to the need to support the educational process with the help of training information systems.