Geodesic
A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data
Matematičeskoe modelirovanie i čislennye metody, no. 9 (2016), pp. 105-122 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Multidimensional continua, large scale data array, multidimensional space of features, deformable cluster, conservation laws for data cluster, forecasting the dynamics of data change, cluster rotation tensor.
Mots-clés : lagrangean coordinates 
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Yu. I. Dimitrienko; O. Yu. Dimitrienko. A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data. Matematičeskoe modelirovanie i čislennye metody, no. 9 (2016), pp. 105-122. http://geodesic.mathdoc.fr/item/MMCM_2016_9_a6/

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