Similarity Classifier with Generalized Mean; Ideal Vector Approach

  • Jouni Sampo
  • Pasi Luukka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


In this paper a study of similarity based classifier with generalized mean and ideal class vector approach is carried out. Before this ideal class vectors in the classifier has been very little investigated area and here focus is changed to study truly ’ideal’ vectors to represent class and similarity measure with its power parameters has been taken from best results in our previous studies. To find correct ideal vectors a search using differential evolution algorithm is carried out.


Differential Evolution Differential Evolution Algorithm Waveform Data Ideal Vector Fuzzy Similarity 
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.
    Zadeh, L.: Similarity Relations and Fuzzy Orderings. Inform Sci. 3 (1971)Google Scholar
  2. 2.
    Luukka, P., Saastamoinen, K.: Similarity Classifier with p-mean and Generalized Łukasiewicz Algebra. International Journal of Hybrid Intelligent Systems (submitted)Google Scholar
  3. 3.
    Luukka, P., Saastamoinen, K., Könönen, V.: A Classifier Based on the Maximal Fuzzy Similarity in the Generalized Łukasiewicz-structure. In: Proceedings of the FUZZ-IEEE 2001 conference, Melbourne, Australia (2001)Google Scholar
  4. 4.
    Saastamoinen, K., Könönen, V., Luukka, P.: A Classifier Based on the Fuzzy Similarity in the Łukasiewicz-Structure with Different Metrics. In: Proceedings of the FUZZ-IEEE 2002 Conference, Hawaii, USA (2002)Google Scholar
  5. 5.
    Saastamoinen, K., Luukka, P.: Classification in the Łukasiewicz Algebra with Different Means. In: Proceedings of FUZZ-IEEE 2003 conference, St Louis, USA (2003)Google Scholar
  6. 6.
    Luukka, P., Meyer, A.: Comparison of two different dimension reduction methods in classification by arithmetic, geometric and harmonic similarity measure. In: Proceedings of FUZZ-IEEE 2004 conference, Budapest, Hungary (2004)Google Scholar
  7. 7.
    Luukka, P., Leppälampi, T.: Similarity classifier with generalized mean applied to medical data using different preprocessing methods. In: Proceedings of the FUZZ-IEEE 2005 conference, Reno, USA (to appear, 2005)Google Scholar
  8. 8.
    UCI Repository of Machine Learning Databases network document. Referenced 4.11.2004. Available:
  9. 9.
    Turunen, E.: Mathematics behind Fuzzy Logic. In: Advances in Soft Computing. Physica-Verlag, Heidelberg (1999)Google Scholar
  10. 10.
    Novak, V.: On the Syntactico-semantical Completeness of First-Order Fuzzy Logic. Kybernetika 26 (1990)Google Scholar
  11. 11.
    Klawonn, F., Castro, J.L.: Similarity in Fuzzy Reasoning. Math Soft. Comp. 2 (1995)Google Scholar
  12. 12.
    Donoho, D.L.: High-dimensional data analysis: The curses and blessings of dimensionality. In: Lecture at the Mathematical Challenges of the 21st Century conference of the American Math. Society, Los Angeles, August 6-11 (2000)Google Scholar
  13. 13.
    Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (1986)Google Scholar
  14. 14.
    Martens, H., Naes, T.: Multivariate Calibration. John Wiley, UK (1989)MATHGoogle Scholar
  15. 15.
    Yao, Y.Y., Wong, S.K.M., Butz, C.J.: On Information-Theoretic Measures of Attribute Importance. In: Pasific-Asia Conference on Knowledge Discovery and Data Mining (1999)Google Scholar
  16. 16.
    Yuan, L., Kesavan, H.K.: Minimum Entropy and Information Measurement. IEEE Transaction on System, Man, and Cybernetics 28(3) (1998)Google Scholar
  17. 17.
    Formato, F., Gerla, G., Scarpati, L.: Fuzzy Subgroups and Similarities. Soft Computing 3 (1999)Google Scholar
  18. 18.
    Coomans, D., Broeckaert, M., Jonckheer, M., Massart, D.L.: Comparison of Multivariate Discriminant Techniques for Clinical Data - Application to the Thyroid Functional State. Meth. Inform. Med. 22, 93–101 (1983)Google Scholar
  19. 19.
    Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)Google Scholar
  20. 20.
    Street, W.N., Wolberg, W.H., Mangasarian, O.L.: Nuclear feature extraction for breast tumor diagnosis. In: IS & T/SPIE 1993 International Symposium on Electronic Imaging: Science and Technology, San Jose, CA, vol. 1905, pp. 861–870 (1993)Google Scholar
  21. 21.
    Smith, J.W., Everhart, J.E., Dickson, W.C., Knowler, W.C., Johannes, R.S.: Using the ADAP learning algorithm to forecast the onset of diabetes mellitus. In: Proceedings of the Symposium on Computer Applications and Medical Care, pp. 261–265 (1988)Google Scholar
  22. 22.
    Bologna, G.: Symbolic Rule Extraction from the DIMLP Neural Network. In: Neural Hybrid Systems. Springer, Heidelberg (to appear)Google Scholar
  23. 23.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
  24. 24.
    Luukka, P.: Similarity measure based classification, PhD thesis, Lappeenranta University of Technology, ISBN 952-214-162-3 (2005)Google Scholar
  25. 25.
    Price, K.V.: Differential Evolution: A Fast and Simple Numerical Optimizer. In: Biennial Conference of the North American (1996)Google Scholar
  26. 26.
    Luukka, P., Sampo, J.: Weighted Similarity Classifier Using Differential Evolution and Genetic Algorithm in Weight Optimization. Journal of Advanced Computational Intelligence and Intelligent Informatics 8(6), 591–598 (2004)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jouni Sampo
    • 1
  • Pasi Luukka
    • 1
  1. 1.Lappeenranta University of TechnologyLappeenrantaFinland

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