**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31515

##### Fractal - Wavelet Based Techniques for Improving the Artificial Neural Network Models

**Authors:**
Reza Bazargan Lari,
Mohammad H. Fattahi

**Abstract:**

Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in grate effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for preprocessing of practical data sets. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based preprocessing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment.

**Keywords:**
Wavelet,
de-noising,
predictability,
time series fractal analysis,
valid length,
ANN.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1094437

**References:**

[1] A. Elshorbagy, S.P. Simonovic, U.S.Panu, "Noise reduction in chaotic hydrologic time series: facts and doubts”, Journal of Hydrology 256 pp.147-165, 2002.

[2] T. Gerstner, H. P. Helfrich, A. Kunoth "Wavelet Analysis of Geoscientific Data Dynamics of multiscale earth systems”, Springer, pp.70-88. 2003.

[3] B. Cannas, A. Fanni, L. See, G. Sias, "Data preprocessing for river flow forecasting using neural networks: Wavelet transforms and data partitioning”, Physics and Chemistry of the Earth 31 pp. 1164–1171, 2006.

[4] G.P. Nason, R. Von Sachs, "Wavelets in time series analysis”, Philosophical Transactions of the Royal Society of London, series A 357 pp. 2511–2526, 1999.

[5] B.B. Mandelbrot, J.W. Van Ness, "Fractional Brownian motions”, fractional noises and applications, SIAM Rev. 10 pp. 422-437, 1968.

[6] A. Eke, P. Hermann, L. Kocsis, L.R. Kozak, "Fractal characterization of complexity in temporal physiological signals”, Physiological Measurement 23 pp.1–38, 2002.

[7] D. Delignieres, S. Ramdani, L. Lemoine, K. Torre, M. Fortes, G. Ninot "Fractal analyses for short time series: A re-assessment of classical methods”, Journal of Mathematical Psychology 50 pp. 525-544, 2006.

[8] C. K.Peng, J. Mietus, J. M. Hausdorff, S Havlin, H. E Stanley, A.L. Goldberger, "Long-range anti-correlations and non-Gaussian behavior of the heartbeat” Physical Review Letter; 70 pp. 1343-1346, 1993.

[9] B. B. Mandelbrot, "The Fractal Geometry of Nature”, W H Freeman publication, New York, 1982.

[10] B.B. Mandelbrot, "Multi fractals and noise”, Wild self-affinity in physics, Springer, New York, 1999.

[11] B. B. Mandelbrot, "Fractals: form, change and dimension”, San Francisco, CA: Freeman publication, New York, 1977.

[12] J. Feder, "Fractal”, Plenum Press, New York, 1988.

[13] F. Pallikari, "A study of the fractal character in electronic noise process”, Chaos, Solitons and Fractals 12 pp. 1499-1507, 2001.

[14] G. Rangrajan, D.A. Sant, "Fractal dimension analysis of Indian climate dynamics”, Chaos,Solitons and Fractals 19 pp.285-291, 2004.

[15] S. Rehman, M. El-Gebeily, "A study of Saudi climate parameters using climate predictability indices”, Chaos, Solitons and Fractals 41(3) pp. 1055-1069, 2009.

[16] M. T. Hagan, H. B. Demuth, M. Beale, "Neural network design”, (2nd Edition), PWS publishing company, Boston, USA, 1996.

[17] M. Nayebi, D. Khalili, S. Amin, Sh. Zand-Parsa, "Daily stream flow prediction capability of artificial neural networks as influenced by minimum air temperature data”, Biosystems and S. Sorooshian. Artificial neural network modeling of the rainfall runoff process Engineering 95(4) pp. 557-567, 2006.

[18] F. Antcil, N. Lauzon, "Generalization for neural networks through data sampling and training procedure, with applications to stream flow predictions”, Hydrology and earth system science 8(5) pp. 940-958, 2004.

[19] N. J. De Vos, T. H. M. Rientjes, "Constraints of artificial neural networks for rainfall-runoff modeling: trade-offs in hydrological state representation and model evaluation”, Hydrology and earth system science 7(5) pp. 693-706, 2005.

[20] I. Daubechies, "Ten Lectures on Wavelets”, CSBM–NSF Series Application Mathematics, vol.61, SIAM publication, Philadelphia, PA. 1992.