Evolution of Multi-class Single Layer Perceptron

  • Sarunas Raudys
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4432)


While training single layer perceptron (SLP) in two-class situation, one may obtain seven types of statistical classifiers including minimum empirical error and support vector (SV) classifiers. Unfortunately, both classifiers cannot be obtained automatically in multi-category case. We suggest designing K(K-1)/2 pair-wise SLPs and combine them in a special way. Experiments using K=24 class chromosome and K=10 class yeast infection data illustrate effectiveness of new multi-class network of the single layer perceptrons.


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  1. 1.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge Univ. Press, Cambridge (2000)Google Scholar
  2. 2.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley, Hoboken (2000)Google Scholar
  3. 3.
    Haykin, S.: Neural Networks: A comprehensive foundation, 2nd edn. Prentice-Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  4. 4.
    Raudys, S.: How good are support vector machines? Neural Networks 13, 9–11 (2000)Google Scholar
  5. 5.
    Raudys, S.: Statistical and Neural Classifiers: An integrated approach to design. Springer, Heidelberg (2001)MATHGoogle Scholar
  6. 6.
    Raudys, S.: Evolution and generalization of a single neurone. I. SLP as seven statistical classifiers. Neural Networks 11, 283–296 (1998)CrossRefGoogle Scholar
  7. 7.
    Raudys, Š., Denisov, V., Bielskis, A.A.: A pool of classifiers by SLP: A multi-class case. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4142, pp. 47–56. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Hsu, C.W., Lin, C.J.: A comparison on methods for multi-class support vector machines. IEEE Trans. on Neural Networks 13, 415–425 (2002)CrossRefGoogle Scholar
  9. 9.
    Le Cun, Y., Kanter, I., Solla, S.: Eigenvalues of covariance matrices: application to neural-network learning. Physical Review Letters 66, 2396–2399 (1991)CrossRefGoogle Scholar
  10. 10.
    Halkaaer, S., Winter, O.: The effect of correlated input data on the dynamics of learning. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9, pp. 169–175. MIT Press, Cambridge (1996)Google Scholar
  11. 11.
    Saudargiene, A.: Structurization of the covariance matrix by process type and block diagonal models in the classifier design. Informatica 10, 245–269 (1999)MATHGoogle Scholar
  12. 12.
    Raudys, S., Saudargiene, A.: First-order tree-type dependence between variables and classification performance. IEEE Trans. on Pattern Analysis and Machine Intelligence 23, 233–239 (2001)CrossRefGoogle Scholar
  13. 13.
    Duin, R.P.W.: Nearest neighbor interpolation for error estimation and classifier optimization. In: Hogd, K.A., Braathen, B., Heia, K. (eds.) Proc. of the 8th Scandinavian Conference on Image Analysis, Tromso, Norway, pp. 5–6 (1993)Google Scholar
  14. 14.
    Skurichina, M., Raudys, S., Duin, R.P.W.: K-NN directed noise injection in multilayer perceptron training. IEEE Trans. on Neural Networks 11, 504–511 (2000)CrossRefGoogle Scholar
  15. 15.
    Raudys, S.: Trainable Fusion Rules. II. Small sample-size effects. Neural Networks 19, 1517–1527 (2006)MATHCrossRefGoogle Scholar
  16. 16.
    Hastie, T., Tibshirani, R.: Classification by pair-wise coupling. The Annals of Statistics 26, 451–471 (1998)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Wu, T.-F., Lin, C.-J., Weng, R.C.: Probability estimates for multi-class classification by pair-wise coupling. J. of Machine Learning Research 5, 975–1005 (2004)MathSciNetGoogle Scholar
  18. 18.
    Giacinto, G., Roli, F., Fumera, G.: Selection of classifiers based on multiple classifier behaviour. In: Amin, A., Pudil, P., Ferri, F.J., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 87–93. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  19. 19.
    Raudys, S.: Trainable Fusion Rules. I. Large sample size case. Neural Networks 19, 1506–1516 (2006)MATHCrossRefGoogle Scholar
  20. 20.
    Pekalska, E., Duin, R.P.W.: Dissimilarity representations allow for building good classifiers. Pattern Recognition Letters 23, 943–956 (2002)MATHCrossRefGoogle Scholar
  21. 21.
    Pizzi, N.J., Pedrycz, W.: Classification of magnetic resonance spectra using parallel randomized feature selection. In: IJCNN04 (2004)Google Scholar
  22. 22.
    Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines (2001), Available at http://www.csie.ntu.edu.tw/~cjlin/libsvm

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Sarunas Raudys
    • 1
  1. 1.Vilnius Gediminas Technical University, Sauletekio 11, Vilnius, LT-10223Lithuania

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