ИСТИНА

In many applied domains, the concept of distance is used for initial formulation and subsequent formalization ofproblems and solution methods. However, for an adequate representation of complex situations, the traditionalconcept of distance is insufficient and richer families of models are required. In this paper, we propose andinvestigate theoretically and empirically one of the families - distances parameterized by size. We also introduce thegeneralized metric axioms as a set of natural requirements in many domains. As examples of applied domains, wecan consider transport systems, in which the transportation time depends on the mass of the cargo, or messagepassing networks, in which the transfer delay depends on the length of the message. The number of combinationsof object couples and sizes is huge, so the complete description of all the situations is data intensive. Then the problem of modelling and approximating the collected dissimilarity tensor is posed and solved in variousways. Several models of distances parameterized by size are proposed in the work. For each of the models,sufficient conditions are found on the parameters (theorems on sufficient conditions) that ensure the fulfillment of allthe generalized metric axioms. To adapt each of the models, we propose a specific method of conditionaloptimization. The idea of some methods is in iterative conditional minimization of the variational upper bound for thestress function, the idea of the last method is in iterative conditional minimization of the quadratic stress function. All the proposed models and methods were implemented and tested on real data on message passing delaysbetween processes in the "Lomonosov" supercomputer system. Experiments have shown a good quality ofapproximation for models with a small number of parameters (that is, a high degree of data compression), as wellas comparability of losses with unconditional problem statements in which the generalized metric axioms areignored.