Abstract
Periodicity analysis of unevenly collected data is a relevant issue in several scientific fields. In astrophysics, for example, we have to find the fundamental period of light or radial velocity curves which are unevenly sampled observations of stars. Classical spectral analysis methods are unsatisfactory to face the problem. In this paper we present a neural network based estimator system which performs well the frequency extraction in unevenly sampled signals. It uses a unsupervised Hebbian nonlinear neural algorithm to extract, from the interpolated signal, the principal components which, in turn, are used by the MUSIC frequency estimator algorithm to extract the frequencies. The neural network is tolerant to noise amplification due to interpolation and, above all, to blank time window in the data. We benchmark the system on realistic and real signals with the Periodogram.
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.
References
Baldi P., Hornik K., Neural networks for principal component analysis: learning from examples without local minima, Neural Networks, 2, (7), 53–58, 1989.
Barone F., Milano L., Russo G., A new method of spectral analysis of unevenly spaced astrophysical data. I. The single-period case, The Astrophysical Journal, 421, 284–302, 1994.
Binnendijk L., The light variation and Orbital Elements of U Pegasi, The Astronomical Journal, 65, (2), 1960.
Brescia M., D’Argenio B., Ferreri V., Longo G., Pelosi N., Rampone S., Tagliaferri R., Neural net aided detection of astronomical periodicities in geologic records, Earth Planetary Science and Letters, 139, 33–45, 1996.
Deeming T. J., Fourier analysis with unequally-spaced data, Astrophysics and Space Science, 36, 137–158, 1975.
Ferraz-Mello S., Estimation of periods from unequally spaced observations, The Astronomical Journal, 86, (4), 1981.
Jutten C., Herault J., Blind separation of sources, parti: an adaptive algorithm based on neuromimetic architecture, Signal Processing, 24, (1), 1–10, 1991.
Home J. H., Baliunas S. L., A prescription for period analysis of unevenly sampled time series, The Astrophysical Journal, 302, 757–763, 1986.
Horowitz L. L., IEEE Trans., ASSP-22, 22, 1974.
Karhunen J., Joutsensalo J., Representation and separation of signals using nonlinear PCA type learning, Neural Networks, 7, 113–127, 1994.
Karhunen J., Joutsensalo J., Generalization of principal component analysis, optimization problems, and neural networks, Neural Networks, 8, 549–562, 1995.
Kay S. M., Modern spectral estimation: theory and application, Englewood Cliffs: Prentice-Hall, 1988.
Lomb N. R., Least-squares frequency analysis of unequally spaced data, Astrophysics and Space Science, 39, 447–462, 1976.
Marple S. L., Digital spectral analysis with applications, Englewood Cliffs: Prentice-Hall, 1987.
Oja E., A simplified neuron model as a principal component analyzer, Journal of Mathematical Biology, 15, 267–273, 1982.
Oja E., Ogawa H., Wangviwattana J., Learning in nonlinear constrained Hebbian network, Artificial neural networks, T. Kohonen, Amsterdam: North-Holland, 385–390, 1991.
Oja E., Karhunen J., Wang L., Vigario R., Principal and independent components in neural networks - recent developments, Seventh Italian Workshop on Neural Networks, Vietri 1995, M.Marinaro & R.Tagliaferri, Singapore: World Scientific Pu., 16–35, 1996.
Oppenheim A. V., Schafer R. W., Digital signal processing, Prentice-Hall, 1965.
Plumbley M., A Hebbian/anti Hebbian network which optimizes information capacity by orthonormalizing the principal subspace, in Proc. IEE Conf. on Artificial Neural Networks, Brighton, UK, 86–90, 1993.
Rasile M., Milano L., Tagliaferri R., Longo G., Neural Networks for periodicity analysis of unevenly spaced data, Proceedings of the 1997 International Conference on Neural Networks ICNN’97, Piscataway, NJ: IEEE, 2257–2262, 1997.
Sanger T. D., Optimal unsupervised learning in a single-layer linear feed-forward network, Neural Network, 2, 459–473, 1989.
Scargle J. D., Studies in astronomical time series analysis; statistical aspects of spectral analysis of unevenly spaced data, The Astrophysical Journal, 263, 835–853, 1982.
Wilson R. E., Devinney E. J., ApJ, 166, 605–614, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag London Limited
About this paper
Cite this paper
Rasile, M., Milano, L., Tagliaferri, R., Longo, G. (1998). Periodicity Analysis of Unevenly Spaced Data by Means of Neural Networks. In: Marinaro, M., Tagliaferri, R. (eds) Neural Nets WIRN VIETRI-97. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1520-5_17
Download citation
DOI: https://doi.org/10.1007/978-1-4471-1520-5_17
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1522-9
Online ISBN: 978-1-4471-1520-5
eBook Packages: Springer Book Archive