The work contains an overview of clustering methods used in the study of gene expression and new results of application of Formal Concepts Analysis to clustering data extracted from the public functional genomics data repository GEO. Methods of Formal Concept Analysis allow clustering of multidimensional data under the single condition of partial ordering of such data sets. As a result, clusters are separate sublattices in the concept lattice, where each sublattice contains hierarchically related formal concepts. This solution of the clustering problem allows deep investigating both mutual influences of genes and their influence on other data obtained in experiments on gene expression. The paper describes a new information technology developed for the implementation of the proposed approach. The technology uses modern solutions in the field of Big Data processing, it has functions for communication with external data sources and other information systems. Preliminary results of the application of this technology to three-dimensional gene expression data obtained from the GEO system are presented.