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Distances Parameterized by Size: Models and Adaptation Techniquesстатья
- Авторы: Maysuradze A., Petrenko D.
- Сборник: Supplementary Proceedings of the XXIII International Conference on Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2021)
- Серия: CEUR Workshop Proceedings (CEUR-WS.org)
- Том: 3036
- Год издания: 2021
- Первая страница: 174
- Последняя страница: 186
- Аннотация: In many domains, the concept of distance is used for initial formulation and subsequent formalization of problems and solution methods. However, for an adequate representation of complex situations, the traditional concept of distance is insufficient, and more expressive families of models are required. In this paper, we propose and investigate theoretically and empirically one of the families — distances parameterized by size. We also introduce the generalized metric axioms as a set of natural requirements in many domains. As examples of applied domains, we can consider transport systems, in which the transportation time depends on the mass of the cargo, or message passing networks, in which the transfer delay depends on the length of the message. The number of combinations of pairs of object and sizes is huge, so the complete description of all the situations is data intensive. The problem of modelling and approximating the collected dissimilarity tensor is posed and solved in various ways. 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 all the generalized metric axioms. To adapt each of the models, we propose a specific method of conditional optimization. The idea of methods is in iterative conditional minimization of the variational upper bound for the stress function. All the proposed models and methods were implemented and tested on real data on message passing delays between processes in the Lomonosov supercomputer system. Experiments have shown a good quality of approximation for models with a small number of parameters (that is, a high degree of data compression), as well as comparability of losses with unconditional problem statements in which the generalized metric axioms are ignored.
- Добавил в систему: Майсурадзе Арчил Ивериевич