Granular Regression

  • B. Apolloni
  • D. Iannizzi
  • D. Malchiodi
  • W. Pedrycz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3931)


We augment a linear regression procedure by a thruth-functional method in order to identify a highly informative regression line. The idea is to use statistical methods to identify a confidence region for the line and exploit the structure of the sample data falling in this region for identifying the most fitting line. The fitness function is related to the fuzziness of the sampled points as a natural extension of the statistical criterion ruling the identification of the confidence region within the Algorithmic Inference approach. We tested the method on three well known benchmarks.


Support Vector Machine Membership Function Gradient Descent Algorithm Radial Basis Function Information Granule 
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.


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  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)MATHGoogle 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)MATHGoogle Scholar
  5. 5.
    Apolloni, B., Malchiodi, D., Gaito, S.: Algorithmic Inference in Machine Learning. In: Advanced Knowledge International, Magill, Adelaide. International series on advanced intelligence, vol. 5 (2003)Google Scholar
  6. 6.
    Cox, E.: The fuzzy systems handbook. AP Professional, San Diego (1998)Google Scholar
  7. 7.
    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
  8. 8.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981)CrossRefMATHGoogle Scholar
  9. 9.
    Aarts, E., Korst, J.: Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing. John Wiley, Chichester (1989)MATHGoogle Scholar
  10. 10.
    National Institute of Standards and Technology: Strd dataset Norris (online accessed April 2005),
  11. 11.
    Mosteller, F., Tukey, J.W.: Data Analysis and Regression: A Second Course in Statistics. Addison-Wesley, Reading Mass (1977)Google Scholar
  12. 12.
    Solar Influence Data Analysis Center, Royal Observatory of Belgium: Sunspot and space weather information pages (online, accessed April 2005),
  13. 13.
    Schölkopf, B., Smola, A.J.: Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • B. Apolloni
    • 1
  • D. Iannizzi
    • 2
  • D. Malchiodi
    • 1
  • W. Pedrycz
    • 3
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di Matematica “F. Enriques”Università degli Studi di MilanoMilanoItaly
  3. 3.Department of Electrical and Computer EngineeringUniversity of Alberta, ECERFEdmontonCanada

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