Imputation of Missing Values by Inversion of Fuzzy Neuro-System

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 391)

Abstract

Incomplete data are common and require special techniques. The essential techniques are: marginalisation, imputation, and rough sets. The paper presents the imputation by inversion of the neuro-fuzzy system. First the neuro-fuzzy systems is trained with complete data. Next the system is inverted and the missing values are imputed. The complete and imputed data are used to train the final neuro-fuzzy system. The technique is limited to data items with one missing value. The paper is accompanied by numerical examples and statistical verification.

Keywords

Evolutionary optimisation Gradient descent Memetic algorithm Big-Bang-Big-crunch 

References

  1. 1.
    Acuña, E., Rodriguez, C.: The treatment of missing values and its effect on classifier accuracy. In: Banks, D., McMorris, F., Arabie, P., Gaul, W. (eds.) Classification, Clustering, and Data Mining Applications, pp. 639–647. Studies in Classification, Data Analysis, and Knowledge Organisation, Springer, Berlin (2004)Google Scholar
  2. 2.
    Batista, G.E.A.P.A., Monard, M.C.: An analysis of four missing data treatment methods for supervised learning. Appl. Artif. Intell. 17(5–6), 519–533 (2003)Google Scholar
  3. 3.
    Box, G.E.P., Jenkins, G.: Time Series Analysis Forecasting and Control. Holden-Day Incorporated, Oakland, California (1970)MATHGoogle Scholar
  4. 4.
    Chen, J.Q., Xi, Y.G., Zhang, Z.J.: A clustering algorithm for fuzzy model identification. Fuzzy Sets Syst. 98(3), 319–329 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cooke, M., Green, P., Josifovski, L., Vizinho, A.: Robust automatic speech recognition with missing and unreliable acoustic data. Speech Commun. 34, 267–285 (2001)CrossRefMATHGoogle Scholar
  6. 6.
    Czogala, E., Leski, J.: Fuzzy and Neuro-Fuzzy Intelligent Systems. Series in Fuzziness and Soft Computing, Physica-Verlag, A Springer-Verlag company, Heidelberg, New York (2000)Google Scholar
  7. 7.
    Filev, D.P.: Inversion of fuzzy models-practical issues. In: ICSFP, vol. 2, pp. 1658–1663. Anchorage, AK (1998)Google Scholar
  8. 8.
    Frank, A., Asuncion, A.: UCI machine learning repository (2010)Google Scholar
  9. 9.
    Gabriel, T.R., Berthold, M.R.: Missing values in fuzzy rule induction. In: SMC, vol. 2, pp. 1473–1476 (2005)Google Scholar
  10. 10.
    Galichet, S., Boukezzoula, R., Foulloy, L.: Explicit analytical formulation and exact inversion of decomposable fuzzy systems with singleton consequents. Fuzzy Sets Syst. 146, 421–436 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Grzymala-Busse, J., Goodwin, L., Grzymala-Busse, W., Zheng, X.: Handling missing attribute values in preterm birth data sets. In: Slezak, D., Yao, J., Peters, J., Ziarko, W., Hu, X. (eds.) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. LNCS, vol. 3642, pp. 342–351. Springer, Berlin (2005)CrossRefGoogle Scholar
  12. 12.
    Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Ras, Z., Zemankova, M. (eds.) Methodologies for Intelligent Systems. LNCS, vol. 542, pp. 368–377. Springer, Berlin (1991)CrossRefGoogle Scholar
  13. 13.
    Hathaway, R., Bezdek, J.: Fuzzy c-means clustering of incomplete data. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 31(5), 735–744 (2001)CrossRefGoogle Scholar
  14. 14.
    Himmelspach, L., Conrad, S.: Fuzzy clustering of incomplete data based on cluster dispersion. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 59–68. Springer, Berlin (2010)Google Scholar
  15. 15.
    Korytkowski, M., Nowicki, R., Scherer, R., Rutkowski, L.: Ensemble of rough-neuro-fuzzy systems for classification with missing features. In: FUZZ-IEEE, pp. 1745–1750. Hong Kong (2008)Google Scholar
  16. 16.
    Kumbasar, T., Eksin, İ., Güzelkaya, M., Yeşil, E.: Big bang big crunch optimization method based fuzzy model inversion. MICAI 2008: Advances in Artificial Intelligence. LNCS, pp. 737–740. Springer, Berlin (2008)Google Scholar
  17. 17.
    Kumbasar, T., Eksin, İ., Güzelkaya, M., Yeşil, E.: Exact inversion of decomposable interval type-2 fuzzy logic systems. Int. J. Approximate Reasoning 54, 253–272 (2013)CrossRefMATHGoogle Scholar
  18. 18.
    Matyja, A., Simiński, K.: Comparison of algorithms for clustering incomplete data. Found. Comput. Decis. Sci. 39(2), 107–127 (2014)Google Scholar
  19. 19.
    Mundfrom, D.J., Whitcomb, A.: Imputing missing values: the effect on the accuracy of classification. Multiple Linear Regres. Viewpoints 25(1), 13–19 (1998)Google Scholar
  20. 20.
    Nowicki, R.K.: Rough-neuro-fuzzy structures for classification with missing data. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 39(6), 1334–1347 (2009)CrossRefGoogle Scholar
  21. 21.
    Ridders, C.: A new algorithm for computing a single root of a real continuous function. IEEE Trans. Circ. Syst. 26, 979–980 (1979)CrossRefMATHGoogle Scholar
  22. 22.
    Sikora, M., Simiński, K.: Comparison of incomplete data handling techniques for neuro-fuzzy systems. Comput. Sci. 15(4), 441–458 (2014)CrossRefGoogle Scholar
  23. 23.
    Sikora, M., Krzykawski, D.: Application of data exploration methods in analysis of carbon dioxide emission in hard-coal mines dewater pump stations. Mechanizacja i Automatyzacja Gornictwa 413(6) (2005)Google Scholar
  24. 24.
    Sikora, M., Sikora, B.: Application of machine learning for prediction a methane concentration in a coal-mine. Arch. Min. Sci. 51(4), 475–492 (2006)Google Scholar
  25. 25.
    Simiński, K.: Neuro-rough-fuzzy approach for regression modelling from missing data. Int. J. Appl. Math. Comput. Sci. 22(2), 461–476 (2012)MATHGoogle Scholar
  26. 26.
    Simiński, K.: Clustering with missing values. Fundamenta Informaticae 123(3), 331–350 (2013)MATHGoogle Scholar
  27. 27.
    Simiński, K.: Rough fuzzy subspace clustering for data with missing values. Comput. Inf. 33(1), 131–153 (2014)Google Scholar
  28. 28.
    Simiński, K.: Rough subspace neuro-fuzzy system. Fuzzy Sets Syst. 269, 30–46 (2015)CrossRefGoogle Scholar
  29. 29.
    Timm, H., Kruse, R.: Fuzzy cluster analysis with missing values. In: NAFIPS, pp. 242–246. Pensacola Beach, FL (1998)Google Scholar
  30. 30.
    Varkonyi-Koczy, A., Almos, A., Kovacshazy, T.: Genetic algorithms in fuzzy model inversion. In: FUZZ-IEEE, vol. 3, pp. 1421–1426 (1999)Google Scholar
  31. 31.
    Wagstaff, K.L., Laidler, V.G.: Making the most of missing values: object clustering with partial data in astronomy. In: ADASS XIV, vol. 347, pp. 172–176. Pasadena, California, USA (2005)Google Scholar
  32. 32.
    Xu, C., Shin, Y.: A fuzzy inverse model construction method for general monotonic multi-input-single-output (MISO) systems. IEEE Trans. Fuzzy Syst. 16(5), 1216–1231 (2008)CrossRefGoogle Scholar
  33. 33.
    Yeh, I.C.: Modeling of strength of high-performance concrete using artificial neural networks. Cement Concr. Res. 28(12), 1797–1808 (1998)CrossRefGoogle Scholar
  34. 34.
    Zhang, S.: Parimputation: from imputation and null-imputation to partially imputation. IEEE Intell. Inf. Bull. 9(1), 32–38 (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of InformaticsSilesian University of TechnologyGliwicePoland

Personalised recommendations