A number of real-world problems of automatic grouping of objects or clustering require a reasonable solution and the possibility of interpreting the result. More specific is the problem of identifying homogeneous subgroups of objects. The number of groups in such a dataset is not specified, and it is required to justify and describe the proposed grouping model. As a tool for interpretable machine learning, we consider formal concept analysis (FCA). To reduce the problem with real attributes to a problem that allows the use of FCA, we use the search for the optimal number and location of cut points and the optimization of the support set of attributes. The approach to identifying homogeneous subgroups was tested on tasks for which interpretability is important: the problem of clustering industrial products according to primary tests (for example, transistors, diodes, and microcircuits) as well as gene expression data (collected to solve the problem of predicting cancerous tumors). For the data under consideration, logical concepts are identified, formed in the form of a lattice of formal concepts. Revealed concepts are evaluated according to indicators of informativeness and can be considered as homogeneous subgroups of elements and their indicative descriptions. The proposed approach makes it possible to single out homogeneous subgroups of elements and provides a description of their characteristics, which can be considered as tougher norms that the elements of the subgroup satisfy. A comparison is made with the COBWEB algorithm designed for conceptual clustering of objects. This algorithm is aimed at discovering probabilistic concepts. The resulting lattices of logical concepts and probabilistic concepts for the considered datasets are simple and easy to interpret.
