Interpolating Support Information Granules

  • B. Apolloni
  • S. Bassis
  • D. Malchiodi
  • W. Pedrycz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4132)


We develop a hybrid strategy combing thruth-functionality, kernel, support vectors and regression to construct highly informative regression curves. The idea is to use statistical methods to form a confidence region for the line and then exploit the structure of the sample data falling in this region for identifying the most fitting curve. The fitness function is related to the fuzziness of the sampled points and is regarded as a natural extension of the statistical criterion ruling the identification of the confidence region within the Algorithmic Inference approach. Its optimization on a non-linear curve passes through kernel methods implemented via a smart variant of support vector machine techniques. The performance of the approach is demonstrated for three well-known benchmarks.


Maximum Likelihood Estimator Fuzzy Regression Information Granule Granular Computing Fuzzy Regression Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pedrycz, W.: Granular computing in data mining. In: Last, M., Kandel, A. (eds.) Data Mining & Computational Intelligence. Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Morrison, D.F.: Multivariate statistical methods, 2nd edn. McGraw-Hill, New York (1989)Google Scholar
  3. 3.
    Poggio, T., Girosi, F.: Networks for approximation and learning. In: Lau, C. (ed.) Foundations of Neural Networks, pp. 91–106. IEEE Press, Piscataway (1992)Google Scholar
  4. 4.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)Google Scholar
  5. 5.
    Seber, G.A.F., Alan, L.J.: Linear Regression Analysis, 2nd edn. Wiley-Interscience, Hoboken (2003)Google Scholar
  6. 6.
    Douglas, B.M., Watts, D.J.: Nonlinear regression analysis and its applications. John Wiley & Sons, New York (1988)MATHGoogle Scholar
  7. 7.
    Tanaka, H., Uejima, S., Asai, K.: Linear regression analysis with fuzzy model. IEEE Transactions Systems, Man and Cybernetic, 903–907 (1982)Google Scholar
  8. 8.
    Savic, D., Pedrycz, W.: Evaluation of fuzzy regression models. Fuzzy Sets and Systems 39, 51–63 (1991)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    U.S. Department Labor Statistics: SMSA dataset. Air pollution and mortality (accessed January 2006),
  10. 10.
    Apolloni, B., Malchiodi, D., Gaito, S.: Algorithmic Inference in Machine Learning. In: Advanced Knowledge International, Magill (2003)Google Scholar
  11. 11.
    Apolloni, B., Bassis, S., Gaito, S., Iannizzi, D., Malchiodi, D.: Learning continuous functions through a new linear regression method. In: Apolloni, B., Marinaro, M., Tagliaferri, R. (eds.) Biological and Artificial Intelligence Environments, pp. 235–243. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981)Google Scholar
  13. 13.
    Aarts, E., Korst, J.: Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing. John Wiley, Chichester (1989)MATHGoogle Scholar
  14. 14.
    Mosteller, F., Tukey, J.: Data Analysis and Regression: A Second Course in Statistics. Addison Wesley, Reading (1977)Google Scholar
  15. 15.
    Apolloni, B., Iannizzi, D., Malchiodi, D., Pedrycz, W.: Granular regression. In: Apolloni, B., Marinaro, M., Nicosia, G., Tagliaferri, R. (eds.) WIRN 2005 and NAIS 2005. LNCS, vol. 3931, pp. 147–156. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • B. Apolloni
    • 1
  • S. Bassis
    • 1
  • D. Malchiodi
    • 1
  • W. Pedrycz
    • 2
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.Department of Electrical and Computer EngineeringUniversity of Alberta, ECERFEdmontonCanada

Personalised recommendations