Abstract
In this paper, a novel Kernel based Soft Computing hybrid viz., Kernel Group Method of Data Handling (KGMDH) is proposed to solve regression problems. In the proposed KGMDH technique, Kernel trick is employed on the input data in order to get Kernel matrix, which in turn becomes input to GMDH. Several experiments are conducted on five benchmark regression datasets to assess the effectiveness of the proposed technique. The results and a statistical t-test conducted thereof indicate that the proposed KGMDH yields more accurate results than the standalone GMDH in most datasets. This is the significant outcome of the study.
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References
Abdel-Aal, R.E.: GMDH-based feature ranking and selection for improved classification of medical data. Journal of Biomedical Informatics 38, 456–468 (2005)
Aizerman, M.A., Braverman, E.M., Rozonoer, L.I.: Theoritical Foundations of the Potential Function Method in Pattern Recognition Learning. Automation and Remote Control 25(6), 821–837 (1964)
Boser, B.E., Guyon, I.M., Vapnik, V.N.: A training algorithm for optimal margin classifiers. In: COLT 1992: Proceedings of the Fifth Annual Workshop on Computational Learning Theory, pp. 144–152. ACM Press, New York (1992)
Farlow, S.J.: Self-Organizing Methods in Modeling: GMDH type Algorithm. Marcel Dekker Inc., New York (1984)
Hilbert, D.: Gruendzugeeiner allgemeinen Theorieder linearen Integralgleichungen (Erste Mitteilung). Nachrichten von der Koenigl. Gesellschaft der Wissenschaften zu Goettingen, Mathematisch-physikalische Klasse (1), 49–91 (1904) (in German)
Ivakhnenko, A.G.: The group method of data handling - a rival of the method of stochastic approximation. Soviet Automatic Control 13(3), 43–55 (1966)
http://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
http://archive.ics.uci.edu/ml/machine-learning-databases/forest-fires/forestfires.csv
http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data
Marcin, W., Jozef, K., Marcin, M., Ron, J.P.: A GMDH neural network-based approach to robust fault diagnosis: applications to the DAMADICS benchmark problem. Control Engineering Practice 14, 671–683 (2006)
Mercer, J.: Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations. Philosophical Transactions of the Royal Society of London. Series A. Containing Papers of a Mathematical or Physical Character 209, 415–446 (1990)
Kordik, P., Naplava, P., Snorek, M., Genyk, M.: The modified GMDH Method Applied to Model Complex System (1982)
Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Muller, K.R.: Fisher Dicriminant Analysis. In: Neural Networks for Signal Processing IX, Proceedings of the 1999 IEEE Signal Processing Society Workshop, pp. 41–48 (1999)
Mohanty, R., Ravi, V., Patra, M.R.: Software Reliability Prediction Using Group Method of Data Handling. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 344–351. Springer, Heidelberg (2009)
Naveen, N., Ravi, V., Raghavendra Rao, C.: Data Mining via Rules Extracted from GMDH: An Application to Predict Churn in Bank Credit Cards. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds.) KES 2010, Part I. LNCS (LNAI), vol. 6276, pp. 80–89. Springer, Heidelberg (2010)
Li, Y., Liu, Y., Zhu, J.: Quantile Regression in Reproducing Kernel Hilbert Spaces. American Statistical Association 102(477) (2007)
Rosipal, R., Trejo, L.J., Cichicki, A.: Kernel principal component regression with EM approach to nonlinear principal components extraction, Technical Report, University of Paisley, Scotland, UK (2000)
Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review 65(6), 386–408 (1958)
Schetinin, V., Schult, J.: Learning polynomial networks for classification of clinical electroencephalograms. Soft Computing 10, 397–403 (2006)
Scholkopf, B., Smola, A.J., Muller, K.R.: Nonlinear component analysis as a kernel eigen value problem. Neural Computation 10(5), 1299–1319 (1998)
Scholkopf, B., Smola, A.J.: Learning with Kernels. MIT Press (2002)
Srinivasan, D.: Energy demand prediction using GMDH networks. Neurocomputing 72(1-3), 625–629 (2008)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Li, Y., Liu, Y., Zhu, J.: Quantile Regression in Reproducing Kernel Hilbert Spaces. American Statistical Association 102(477) (2007)
Zhu, J., Hastie, T.: Kernel logistic regression and the import vector machine. In: Advances in Neural Information Processing Systems, vol. 14 (2001)
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Reddy, K.N., Ravi, V. (2012). Kernel Group Method of Data Handling: Application to Regression Problems. In: Panigrahi, B.K., Das, S., Suganthan, P.N., Nanda, P.K. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2012. Lecture Notes in Computer Science, vol 7677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35380-2_10
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DOI: https://doi.org/10.1007/978-3-642-35380-2_10
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