On Some Factorizations of Semi-Metric Cones and Quality Estimates of Heuristic Metrics in Data Analysis Problems

An approach is proposed to consider heuristic metrics introduced and used in data analysis problems. In the approach, the entire information on pairwise distances expressed by numerical values is reduced to information on a metric belonging as a point of a semi-metric cone to corresponding subcones, which are elements of factor sets for proposed relations of kernel equivalences for mappings into formal index families.