Abstract
Rough-neuro-fuzzy systems offer suitable way for classifying data with missing values. The paper presents a new implementation of gradient learning in the case of missing input data which has been adapted for rough-neuro-fuzzy classifiers. We consider the system with singleton fuzzification, Mamdani-type reasoning and center average defuzzification. Several experiments based on common benchmarks illustrating the performance of trained systems are shown. The learning and testing of the systems has been performed with various number of missing values.
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References
Rubin, D.B.: Interference and missing data. Biometrika 63, 581–592 (1976)
Little, R.J.A., Rubin, D.B.: Statistical analysis with missing data, 2nd edn. Wiley–Interscience (2002)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B 39, 1–38 (1977)
Song, Q., Shepperd, M., Chen, X., Liu, J.: Can k-nn imputation improve the performance of c4.5 with small software project data sets? a comparative evaluation. The Journal of Systems & Software 81(12), 2361–2370 (2008)
Walczak, B., Massart, D.L.: Dealing with missing data: Part i. Chemometrics and Intelligent Laboratory Systems 58(1), 15–27 (2001)
Sartori, N., Salvan, A., Thomaseth, K.: Multiple imputation of missing values in a cancer mortality analysis with estimated exposure dose. Computational Statistics and Data Analysis 49(3), 937–953 (2005)
Nowicki, R.: Rough–neuro–fuzzy structures for classification with missing data. IEEE Trans. on Systems, Man, and Cybernetics—Part B: Cybernetics 39 (2009)
Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Sowiski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 203–232. Kluwer, Dordrecht (1992)
Nowicki, R.K.: On combining neuro–fuzzy architectures with the rough set theory to solve classification problems with incomplete data. IEEE Trans. on Knowledge and Data Engineering 20(9), 1239–1253 (2008)
Rutkowski, L.: New Soft Computing Techniques for System Modeling, Pattern Classification and Image Processing. Springer, Heidelberg (2004)
Mertz, C.J., Murphy, P.M.: UCI respository of machine learning databases, http://www.ics.uci.edu/pub/machine-learning-databases
Korytkowski, M., Rutkowski, L., Scherer, R.: From Ensemble of Fuzzy Classifiers to Single Fuzzy Rule Base Classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008)
Scherer, R.: Boosting Ensemble of Relational Neuro-fuzzy Systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 306–313. Springer, Heidelberg (2006)
Korytkowski, M., Scherer, R., Rutkowski, L.: On combining backpropagation with boosting. In: 2006 International Joint Conference on Neural Networks, Vancouver, BC, Canada, pp. 1274–1277 (2006)
Scherer, R.: Neuro-fuzzy Systems with Relation Matrix. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS, vol. 6113, pp. 210–215. Springer, Heidelberg (2010)
Rutkowski, L., Cpałka, K.: A general approach to neuro - fuzzy systems. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, December 2-5, vol. 3, pp. 1428–1431 (2001)
Rutkowski, L., Cpałka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control and Cybernetics 31(2), 297–308 (2002)
Starczewski, J., Rutkowski, L.: Interval type 2 neuro-fuzzy systems based on interval consequents. In: Rutkowski, L., Kacprzyk, J. (eds.) Neural Networks and Soft Computing, pp. 570–577. Physica-Verlag, Springer-Verlag Company, Heidelberg, New York (2003)
Starczewski, J., Rutkowski, L.: Connectionist Structures of Type 2 Fuzzy Inference Systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 634–642. Springer, Heidelberg (2002)
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Nowak, B.A., Nowicki, R.K. (2012). Learning in Rough-Neuro-Fuzzy System for Data with Missing Values. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_51
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DOI: https://doi.org/10.1007/978-3-642-31464-3_51
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