Article 1316

Title of the article

MODEL-BASED PRESENTATIONS OF DATA ON THE BASIS OF DIRECT TENSOR CALCULUS

Authors

Makarychev Petr Petrovich, Doctor of engineering sciences, professor, head of sub–department of computer application and software, Penza State University (40 Krasnaya street, Penza, Russia), makpp@yandex.ru
Artamonov Dmitriy Vladimirovich, Doctor of engineering sciences, professor, sub-department of autonomous information and control systems, Penza State University (40 Krasnaya street, Penza, Russia), aius@pnzgu.ru

Index UDK

681.3

DOI

10.21685/2072-3059-2016-3-1

Abstract

Background. In information systems, data analyses are usually performed from the point of view of the plurality of measurements. Conceptual model representations are based on concepts such as an object, a class, a relation. For a formalized description of data one uses matrix calculus, algebra of tuples and tensor calculus.
Materials and methods. Data can be presented in the form of a generalized ten-sor model, which may be interpreted in different subject areas.
Results. The authors developed a model of representation of classes, objects and relationships of the subject space of information systems. The model has a direct tensor notation of relations, arithmetic and logical operations. Classes (objects) of the subject space are defined in the form of dyads that characterize the object space. The subject spaces "Star", "Snowflake" and "Constellation" are specified in the form of tensors of the second order – disordered aggregate dyads associated with the classes. The researchers developed a tensor representation of queries in relational data structures, arithmetic and logical operations, reviewed procedures for data processing and analysis, and described an example of cluster analysis implementation.
Conclusions. The authors have suggested the tensor model representation of relational data structures. The representation provides formalized description of simple and complicated queries to databases, arithmetic and logical operations, procedures of data processing and analysis.

Key words

data model, tensor calculus, dyad, invariant, tensors ratio, tensors predicate.

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References

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Дата создания: 07.02.2017 08:22
Дата обновления: 07.02.2017 16:19