Nonlinear methods of analysis of data with gaps

• Autorzy: Dergachev V. A. , Makarenko N. G. , Karimova L. N. , Danilkina E. B.
• Języki publikacji: EN

Abstrakty

EN

Information on most of natural phenomena can be obtained from time series of direct and proxy data. The analysis of time series generated by natural dynamic systems is a key element in interpreting geophysical and climatic information. Unfortunately, most of available time series have gaps. When there are many gaps with irregular distribution, we do not have any statistical tools for repairing the data. We suggest some approach to solve this problem. It is based on modeling the missing data by small-dimensional manifolds and neural network technologies. In this approach we assume that data under consideration are a set of n-dimensional vectors, which are produced by dynamical system. These vectors model n-dimensional attractor in embedding space. Gaps in the vectors are represented as a linear manifold L of some dimension. The method idea is to model L by another small-dimensional manifold, e.g. a curve. Neural networks are used to find this manifold. We verify the method on real time series data: sunspot numbers, the radiocarbon content in tree rings, the 10Be in ice cores, the width of tree rings and so on.

Słowa kluczowe

EN

neural network; attractor; natural time series; modeling; radiocarbon concentration; tree-ring width; Wolf number; sea level; berillium-10 content

• Wydawca: De Gruyter
• Czasopismo: Geochronometria
• Rocznik: 2001
• Tom: Vol. 20
• Strony: 45--50
• Opis fizyczny: Bibliogr. 12 poz., tab. wykr.

Twórcy

autor

Dergachev V. A.

• Ioffe Physico-Technical Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia

autor

Makarenko N. G.

• Institute of Mathematics, Almaty, 4801100 Kazakstan

autor

Karimova L. N.

• Institute of Mathematics, Almaty, 4801100 Kazakstan

autor

Danilkina E. B.

• Institute of Mathematics, Almaty, 4801100 Kazakstan

Bibliografia

• 1. Beer J., Baumgartner St., Dittrich-Hannen B., Hauenstein J., Kubik P., Lukasczyk Ch., Mende W., Stellmacher R. and Suter M., 1994: Solar variability traced by cosmogenic isotopes. In: Pap J.M., Frohlich C., Hudson H.S. and Solanki S.K., eds., The Sun as a Variable Star: Solar and Stellar Irradiance Variations, Cambridge University Press: 291-300.
• 2. Danilkina E.B., Kuandykov Y.B. and Makarenko N.G., 2001: The neural networks and chaos in the problem of non-complete data reconstruction (in Russian). Neuroinformatics-2001, Moscow, MIFI: 166-173.
• 3. Dergachev V.A., Makarenko N.G., Kuandykov E.B. and Rossiev A.A., 2001: How to discover interrelation between two dynamical systems using observed time series with gaps (in Russian).Izvestiya Academii Nauk, Seriya Fizicheskaya 65(3): 391-393.
• 4. Eckmann J.P. and Ruelle D., 1985: Ergodic theory of chaos and strange attractors. Review of Modern Physics 57(3): 617-656.
• 5. Gorban A.A., Rossiev A.A. and Wunsch II D.C., 2000: Self-organizing curves and modeling by neural networks of data with gaps (in Russian). Neuroinformatics-2000, Moscow, MIFI: 40-46.
• 6. Gorban A.A. and Rossiev A.A., 2000: Iterative Modeling Data with Gaps by Self-organizing Small-dimensional Manifolds with the help of Neural Networks (in Russian). Neuroinformatics and its Applications, Proceedings of VIII Seminar, October 6-8, 2000, Krasnoyarsk: 45-48.
• 7. Kennel M.B., Brown R. and Abarbanel H.D.I., 1992: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A 45: 3403 -3411.
• 8. Little R.J.A. and D.B. Rubin., 1987: Statistical Analysis with Missing Data. John Willey and Sons.
• 9. Lovelius N.V., 1997: Dendroindication of natural processes and anthropogenic influences. World and Family-95, St.Petersburg: 320 p.
• 10. Sadykov Zh.S., Golubtsov V.V. and Duisenbaev Zh.D., 1995: Changes of the Caspian Sea level and its prediction (in Russian). Doklady Academy Nauk Kazakhstan Respublika 6: 9-19.
• 11. Sauer T., Yorke J.A. and Casdagli M., 1991: Embedology. Journal of Statistical Physics 65(3/4): 579-616.
• 12. Stuiver M. and Becker B., 1993: High precision decadal calibration of the radiocarbon time scale AD 1950-6000 BC. Radiocarbon 35 (1): 35-65.