Abstract
We propose an application of SVD model reduction to the class of RBF neural models for improving performance in contexts such as on-line prediction of time series. The SVD is coupled with QR-cp factorization. It has been found that such a coupling leads to more precise extraction of the relevant information, even when using it in an heuristic way. Singular Spectrum Analysis (SSA) and its relation to our method is also mentioned. We analize performance of the proposed on-line algorithm using a ‘benchmark’ chaotic time series and a difficult-to-predict, dynamically changing series.
Research partially supported by the Spanish MCyT Projects TIC2001-2845, TIC2000-1348 and DPI2001-3219.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
[BCC+97]_L.S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R.C. W Haley. “ScaLAPACK User’s Guide”. SIAM Publications. Philadelphia, U.S.A. (1997).
A. Björck. “Numerical Methods for Least Squares Problems”. SIAM Publications. Philadelphia, U.S.A. (1996).
D.S. Broomhead and G.P. King. Extracting qualitative dynamics from experimental data. Physica D 20, 217–236 (1986).
R.P. Brent and F.T. Luk. The solution of singular value and symmetric eigenvalue problems on multiprocessor arrays. SIAM Journal on Scientific and Statistical Computing 6, 69–84 (1985).
J.B. Elsner and A.A. Tsonis. “Singular Spectrum Analysis: A New Tool in Time Series Analysis”. Plenum Press. New York, U.S.A. (1996).
G.H. Golub and C.F. Van Loan. “Matrix Computations”. The Johns Hopkins University Press. Baltimore, Maryland, U.S.A., third edition (1996).
N. Golyandina, V. Nekrutkin, and A. Zhigljavsky. “Analysis of Time Series Structure: SSA and Related Techniques”. Chapman & Hall/CRC Press. Boca Raton, Florida, U.S.A. (2001).
J. Moody and C. J. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation 1, 281–294 (1989).
J. Platt. A resource allocating network for function interpolation. Neural Computation 3, 213–225 (1991).
D.S.G. Pollock. “A Handbook of Time Series Analysis, Signal Processing and Dynamics”. Academic Press. London, U.K. (1999).
M. Salmeron. “Time Series Prediction with Radial Basis Neural Network and Matrix Decomposition Techniques. PhD thesis (in spanish)”. Department of Computer Architecture and Computer Technology. University of Granada, Spain (2001).
[SOP+02]_M. Salmeron, J. Ortega, A. Prieto, C.G. Puntonet, M. Damas, and I. Rojas. High-Performance time series prediction in a cluster of Computers. Concurrency and Computation: Practice & Experience (submitted) (2002).
M. Salmeron, J. Ortega, C.G. Puntonet, and A. Prieto. Improved RAN sequential prediction using orthogonal techniques. Neurocomputing 41(1-4), 153–172 (2001).
G.W. Stewart. “Matrix Algorithms-Volume II: Eigensystems”. SIAM Publications. Philadelphia, U.S.A. (2001).
A.S. Weigend and N.A. Gershenfeld. “Time Series Prediction: Forecasting the Future and Understanding the Past”. Addison-Wesley. Reading, Massachusetts (1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salmerón, M., Ortega, J., Puntonet, C.G., Prieto, A., Rojas, I. (2002). SSA, SVD, QR-cp, and RBF Model Reduction. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_96
Download citation
DOI: https://doi.org/10.1007/3-540-46084-5_96
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44074-1
Online ISBN: 978-3-540-46084-8
eBook Packages: Springer Book Archive