On the formation of sets of precedents based on tables of heterogeneous feature descriptions by methods of topological theory of data analysis

Factorization of the contributions of various variables in the analysis of heterogeneous feature descriptions is an urgent task of complex data mining. The paper proposes the development of the lattice formalism of the topological theory of data analysis, within which new methods for generating parametric estimates and metrics on lattices formed over the topologies of sets of objects are obtained. The formalism was tested on the problem of forming sets of precedents for conducting chemomicrobiome analysis. Whereas the generation of a set of initial information based on regression coefficients and the difference in the values of the learning material corresponded to an extremely low generalizing ability of custom algorithms (correlation coefficient in the control $0.32 \pm 0.20$), the use of the proposed estimates for generating sets of precedents in chemomicrobiomics problems made it possible to significantly increase the generalizing ability of the corresponding algorithms (correlation coefficient in control $0.79\pm 0.21$).