Nonlinear principal component analysis by neural networks: Theory and application to the Lorenz system

Journal of Climate

Volumn 13, Issue 4, 2000, Pages 821-835

  Monahan, Adam H ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA REDUCTION; FEATURE EXTRACTION; FEEDFORWARD NEURAL NETWORKS; STATISTICAL METHODS;

LORENTZ ATTRACTOR; LORENTZ SYSTEM; NONLINEAR PRINCIPAL COMPONENT ANALYSIS;

CLIMATOLOGY;

ARTIFICIAL NEURAL NETWORK; PRINCIPAL COMPONENT ANALYSIS;

EID: 0343191447     PISSN: 08948755     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0442(2000)013<0821:NPCABN>2.0.CO;2     Document Type: Article

References (30)

1. Banfield, J. D., and A. E. Raferty, 1992: Ice floe identification in satellite images using mathematical morphology and clustering about principal curves. J. Amer. Stat. Assoc., 87, 7-16.
2. Barnston, A. G., and R. E. Livezey, 1987: Classification, seasonality, and persistence of low-frequency atmospheric circulation patterns. Mon. Wea. Rev., 115, 1083-1126.
3. _, and C. F. Ropelewski, 1992: Prediction of ENSO episodes using canonical correlation analysis. J. Climate, 5, 1316-1345.
4. Berliner, L. M., 1992: Statistics, probability, and chaos. Stat. Sci., 7, 69-122.
5. Bishop, C. M., 1995: Neural Networks for Pattern Recognition. Clarendon Press, 482 pp.
6. Cybenko, G., 1989: Approximation by superpositions of a sigmoidal function. Math. Contrib. Signals Syst., 2, 303-314.
7. De Mers, D., and G. Cottrell, 1993: Nonlinear dimensionality reduction. Neural Inform. Proc. Syst., 5, 580-587.
8. Dong, D., and T. J. McAvoy, 1996: Nonlinear principal component analysis - Based on principal curves and neural networks. Comp. Chem. Eng., 20, 65-78.
9. Finnoff, W., F. Hergert, and H. G. Zimmermann, 1996: Improving model selection by nonconvergent methods. Neural Networks, 6, 771-783.
10. Fotheringhame, D., and R. Baddeley, 1997: Nonlinear principal components analysis of neuronal spike train data. Biol. Cybernetics, 77, 282-288.
11. Hastie, T., and W. Steutzle, 1989: Principal curves. J. Amer. Stat. Assoc., 84, 502-516.
12. _, and R. J. Tibshirani, 1990: Generalised Additive Models. Chapman and Hall, 335 pp.
13. Hsieh, W. W., and B. Tang, 1998: Applying neural network models to prediction and data analysis in meteorology and oceanography. Bull. Amer. Meteor. Soc., 79, 1855-1870.
14. Kramer, M. A., 1991: Nonlinear principal component analysis using autoassociative neural networks. AIChE J., 37, 233-243.
15. Le Blanc, M., and R. Tibshirani, 1994: Adaptive principal surfaces. J. Amer. Stat. Assoc., 89, 53-64.
16. Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. MIT Department of Meteorology, Statistical Forecast Project Rep. 1, 49 pp. [Available from Dept. of Meteorology, MIT, Massachusetts Ave., Cambridge, MA 02139.]
17. _, 1963: Deterministic aperiodic flow. J. Atmos. Sci., 20, 131-141.
18. Malthouse, E. C., 1998: Limitations of nonlinear PCA as performed with generic neural networks. IEEE Trans. Neural Networks, 9, 165-173.
19. Miller, A. J., W. B. White, and D. R. Cayan, 1997: North Pacific thermocline variations on ENSO timescales. J. Phys. Oceanogr., 27, 2023-2039.
20. Mo, K. C., and M. Ghil, 1987: Statistics and dynamics of persistent anomalies. J. Atmos. Sci., 44, 877-901.
21. North, G. R., 1984: Empirical orthogonal functions and normal modes. J. Atmos. Sci., 41, 879-887.
22. Oja, E., 1997: The nonlinear PCA learning rule in independent component analysis. Neurocomputing, 17, 25-45.
23. _, and J. Karhunen, 1993: Nonlinear PCA: Algorithms and applications. Helsinki University of Technology Tech. Rep. A18. 25 pp. [Available from Laboratory of Computer and Information Sciences, Helsinki University of Technology, Rakentajanaukio 2C, SF-02150, Espoo, Finland.]
24. Preisendorfer, R. W., 1988: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 425 pp.
25. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in C. Cambridge University Press, 994 pp.
26. Sanger, T., 1989: Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks, 2, 459-473.
27. Sengupta, S. K., and J. S. Boyle, 1995: Nonlinear principal component analysis of climate data. PCMDI Tech. Rep. 29, 21 pp. [Available from Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, University of California, Livermore, CA 94550.]
28. Tangang, F. T., B. Tang, A. H. Monahan, and W. W. Hsieh, 1998: Forecasting ENSO events: A neural network - Extended EOF approach. J. Climate, 11, 29-41.
29. von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 494 pp.
30. Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.