539.3+519.86 A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data

Dimitrienko Y. I. (Bauman Moscow State Technical University), Dimitrienko O. Y. (Bauman Moscow State Technical University)

MULTIDIMENSIONAL CONTINUA, LARGE SCALE DATA ARRAY, MULTIDIMENSIONAL SPACE OF FEATURES, LAGRANGEAN COORDINATES, DEFORMABLE CLUSTER, CONSERVATION LAWS FOR DATA CLUSTER, FORECASTING THE DYNAMICS OF DATA CHANGE, CLUSTER ROTATION TENSOR.


doi: 10.18698/2309-3684-2016-1-105122


The article considers the concept of applying the multidimensional continuum model to one of the main problems emerging in the theory of large scale data array treatment i.e. forecasting the dynamics of data cluster change. The concept is based on the model of multidimensional continua in spaces of high dimensionality (more than three) earlier developed by the authors. The model includes the integral conservation laws, which are reformulated for informational data clusters, as well as the model of motion kinematics and cluster deformation. The model of deformable multidimensional cluster is developed. The movement of the cluster in multidimensional data space includes translational and rotational motion and uniform tension-compression strain. The system of differential tensor equations describing the dynamics of the deformable multivariate cluster motion over time is formulated. A numerical algorithm for solving the system of differential equations for the ellipsoidal model of multidimensional cluster is worked out. An example of the developed model application for predicting the dynamics of economic data (data on goods purchases in a large supermarket) is considered. The results of forecasting the data on purchases of different consumer groups are shown.


[1] Shipunov A.B., Baldin E.M., Volkova P.A., Korobeinikov A.I., Nazarova S.A., Petrov S.V., Sufiyanov V.G. Naglyadnaya statistika. Ispolzuem R! [Visual Statistics. Use R!]. DMK Press Publ., 2014, 298 p. ISBN 978-5-94074-828-1.
[2] Demin I.S. Klasterizatsiya kak instrument intellektualnogo analiza dannykh [Clustering as a Tool of Intellectual Data Analysis]. Novye informatsionnye tekhnologii v obrazovanii, Chast 1 [New Information Technologies in Education. Part 1], Moscow, 1S-Publishing, 2011, pp. 98–103.
[3] Demin I. S. Klasterizatsiya ravnomerno raspredelennykh mnozhestv metodami neyronnykh setey [Clustering Uniformly Distributed Sets by Methods of Neural Networks]. Modeli ekonomicheskikh sistem i informatsionnye tekhnologii [Models of Economic Systems and Information Technology], Moscow, Finansovaya akademiya Publ., 2007, pp. 34–38.
[4] Oreshkov V.I. Kreativnaya ekonomika — Creative Economics, 2011, no. 12, pp. 84–89.
[5] Zhuravlev Yu.I., Ryazanov V.V., Senko O.V. Raspoznavanie. Matematichaskie metody. Programmnaya sistema. Prakticheskie primenenia [Recognition. Mathematical Methods. Software system. Practical Applications]. Moscow, “Phazis” Publ., 2006, 176 p. ISBN 5-7036-0108-8.
[6] Aivazyan S.A., Bukhshtaber V.M., Enukov I.S., Meshalkin L.D. Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti [Applied Statistics. Classification and Dimension Reduction]. Moscow, Finansy i statistika Publ., 1989.
[7] Barsegyan A.A., Kupriyanov M.S., Stepanenko V.V., Kholod I.I. Metody i modeli analiza dannykh: OLAP and Data Mining [Methods and Models of Data Analysis: OLAP and Data Mining]. St. Petersburg, BKhV-Peterburg Publ., 2004.
[8] Han J., Kamber M. Data mining: Concepts and Techniques. Morgan Kaufmann Publ., 2001.
[9] Konar A. Artificial intelligence and soft computing: behavioral and cognitive modeling of the human brain. Boca Raton, Florida, CRC Press LLC Publ., 2000.
[10]Mitra S., Acharya T. Data Mining. Multimedia, Soft Computing, and Bioinformatics. Hoboken, New Jersey, John Wiley & Sons Inc. Publ., 2003.
[11]Dimitrienko O.Yu. Informatsionnye Tekhnologii — Information Technologies, 2007, no. 11, pp. 74–80.
[12]Dimitrienko Yu.I., Dimitrienko O.Yu. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2010, no. 3, pp. 56–71.
[13]Dimitrienko Yu.I., Dimitrienko O.Yu. Doklady Akademii Nauk — Doklady Mathematics, 2010, vol. 435, no. 4, pp. 466–469.
[14]Dimitrienko Yu.I., Dimitrienko O.Yu. Informatsionnye Tekhnologii — Information Technologies, 2010, no. 8, pp. 54–62.
[15]Dimitrienko Yu.I., Dimitrienko O.Yu. Doklady Mathematics, 2010, vol. 82, no. 3, pp. 982–985.
[16]Dimitrienko Yu.I., Dimitrienko O.Yu. Doklady Akademii Nauk — Doklady Mathematics, 2011, vol. 440, no. 2, pp. 168–171.
[17]Dimitrienko Yu.I., Dimitrienko O.Yu. Informatsionnye Tekhnologii — Information Technologies, 2012, no. 1, рр. 55–61.
[18]Dimitrienko Yu.I. Nelineinaya mekhanika sploshnoi sredy [Nonlinear Continuum Mechanics]. Moscow, Fizmatlit Publ., 2009, 624 p.
[19]Dimitrienko Yu.I. Mekhanika sploshnoi sredy. V 4 tomakh. Tom 1. Tenzornyi analiz [Continuum mechanics. In 4 vols. Vol. 1. Tensor analysis]. Moscow, BMSTU Publ., 2011, 367 p.
[20]Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor Calculus]. Moscow, Vysshaya shkola Publ., 2001, 575 p.
[21]Zhileikin M.M., Sarach E.B. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2015, no. 3, pp. 17–40.
[22]Zinovyev A.Yu. Vizualizatsia mnogomernykh dannykh [Visualization of Multidimensional Data]. Krasnoyarsk, Krasnoyarsk State Technical University Publ., 2000, 180 p.


Dimitrienko Y., Dimitrienko O. A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 105-122



Download article

Колличество скачиваний: 176