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Factorial modeling using neural network
Matematičeskoe modelirovanie i čislennye metody, no. 10 (2016), pp. 85-103 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the factorial modeling of the initial stage arterial hypertension. The modeling was carried out by the factorization method based on the neural network and the back propagation of error algorithm. This factorization method is an alternative to the classical factor analysis. We implemented an algorithm for constructing the factorial structure based on the neural network in software. This method has been improved for the factor rotation and obtaining an interpretable solution. The hypertension factorial structure obtained by this factorization method is in accordance with the results of the factorial modeling by other methods.
Keywords: Arterial hypertension, factor analysis, neural networks, back propagation of error. 
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V. A. Shovin; V. V. Goltiapin. Factorial modeling using neural network. Matematičeskoe modelirovanie i čislennye metody, no. 10 (2016), pp. 85-103. http://geodesic.mathdoc.fr/item/MMCM_2016_10_a5/

[1] Iberla K., Factor analysis, Statistika Publ., Moscow, 1980

[2] Gavrilkevich M., Introduction to neuro mathematics, vol. 1, Review of applied and industrial mathematics, iss. 3, pp. pp.

[3] Hornik K., Stinchcombe M., White H., “Multilayer Feedforward Networks are Universal Approximators”, Neural Networks, 2:5 (1989), 359–366

[4] Cybenko G., Approximation by Superpositions of a Sigmoidal Function, Signals and Systems, Mathematics of Control, 1989, 314 pp.

[5] Funahashi K., “On the Approximate Realization of Continuous Mappings by Neural Networks”, Neural Networks, 2:3 (1989)

[6] Gorban A.N., Siberian Journal of Numerical Mathematics, 1:1 (1998), 11–24

[7] Haykin S., Neural networks: A Comprehensive Foundation, Vilyams Publ., Moscow, 2008, 1103 pp.

[8] Osovskiy S., Neural networks for information processing, Finansy i statistika Publ., Moscow, 2002, 344 pp.

[9] Gorban A., Kegl B., Wunsch D., Zinovyev A., Principal Manifolds for Data Visualisation and Dimension Reduction, Springer,, Berlin, 2007

[10] Kruger U., Antory D., Hahn J., Irwin G.W., McCullough G., “Introduction of a nonlinearity measure for principal component models”, Computers Chemical Engineering, 2005, no. 2, 2355–2362

[11] Jain A.K., Mao J., Mohiuddin K.M., “Artificial Neural Networks: A Tutorial”, Computer, 29:3 (1996), 31–44

[12] Shovin V.A., Goltyapin V.V., Mathematical Structures and Modeling, 2015, no. 2, 75–84

[13] Goltyapin V.V., Shovin V.A., Herald of Omsk University, 2010, no. 4, 120–128

[14] Shovin V.A., Computer Research and Modeling, 4:4 (2012), 885–894

[15] Martynenko S.I., Mathematical Modeling and Computational Methods, 2015, no. 6, 105–120