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Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology

Gorban, Prof. Alexander. N. and Zinovyev, Dr. Andrei Yu. (2001) Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology. [Preprint]

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Abstract

Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real economical, sociological and biological datasets and to some model data distributions. The basic of the technology is original idea of elastic net - regular point approximation of some manifold that is put into the multidimensional space and has in a certain sense minimal energy. This manifold is an analogue of principal surface and serves as non-linear screen on what multidimensional data are projected. Remarkable feature of the technology is its ability to work with and to fill gaps in data tables. Gaps are unknown or unreliable values of some features. It gives a possibility to predict plausibly values of unknown features by values of other ones. So it provides technology of constructing different prognosis systems and non-linear regressions. The technology can be used by specialists in different fields. There are several examples of applying the method presented in the end of this paper.

Item Type:Preprint
Additional Information:Free software for data visualization is available online: http://www.ihes.fr/~zinovyev/ Contact information: E.mail: agorban@mat.ethz.ch, zinovyev@ihes.fr
Keywords:Vizualization, Data mining, Neural networks, Self-organizing maps, Genomic
Subjects:Computer Science > Neural Nets
ID Code:3082
Deposited By: Gorban, Prof Alexander N.
Deposited On:25 Jul 2003
Last Modified:11 Mar 2011 08:55

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1. Gorban A. N., Zinovyev A.Yu., Pitenko A. A. Visualization of data using method of elastic maps. Informatsionnie technologii, 'Mashinostrornie' Publ., Moscow, 2000. ?6, pp.26-35.

2. Gorban A.N., Rossiev A.A. Method of principal curves for data with gaps. Proc. of 12th international conference "Problems of neurocybernetics". Rostov-Na-Donu, Russia, 1999. pp. 198-201.

3. Kivimoto K. Topology Preservation in SOM. Proc. of International Conference on Neural NetWorks. Washington, DC, 1996. Vol.1. PP. 294-300.

4. Kohonen T. Self-Organizing Maps. Springer: Berlin - Heidelberg, 1997.

5. Shumsky S. A., Kochkin A.N. Self-Organizing maps of financial indicators of the 200 biggest Russian companies. Proc. of All-Russia science conference "NeuroInformatics-99". Moscow, 1999. Part 3. P. 122-127.

6. Zinovyev A. Yu. Visualization of Multidimensional Data. Krasnoyasrk State Technical University Press, 2000. 168 p.

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