On the Use of Hyperspheres in Artificial Immune Systems as Antibody Recognition Regions

  • Thomas Stibor
  • Jonathan Timmis
  • Claudia Eckert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4163)


Using hyperspheres as antibody recognition regions is an established abstraction which was initially proposed by theoretical immunologists for use in the modeling of antibody-antigen interactions. This abstraction is also employed in the development of many artificial immune system algorithms. Here, we show several undesirable properties of hyperspheres, especially when operating in high dimensions and discuss the problems of hyperspheres as recognition regions and how they have affected overall performance of certain algorithms in the context of real-valued negative selection.


False Alarm Rate Anomaly Detection Repertoire Size Monte Carlo Integration Unitary Hypercube 
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.
    Perelson, A.S., Oster, G.F.: Theoretical studies of clonal selection: minimal antibody repertoire size and reliability of self-nonself discrimination. J. Theor. Biol. 81, 645–670 (1979)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Percus, J.K., Percus, O.E., Perelson, A.S.: Predicting the size of the t-cell receptor and antibody combining region from consideration of efficient self-nonself discrimination. Proceedings of National Academy of Sciences USA 90, 1691–1695 (1993)CrossRefGoogle Scholar
  3. 3.
    de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Heidelberg (2002)MATHGoogle Scholar
  4. 4.
    González, F., Dasgupta, D., Niño, L.F.: A randomized real-valued negative selection algorithm. In: Timmis, J., Bentley, P.J., Hart, E. (eds.) ICARIS 2003. LNCS, vol. 2787, pp. 261–272. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Ji, Z., Dasgupta, D.: Real-valued negative selection algorithm with variable-sized detectors. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 287–298. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Stibor, T., Timmis, J.I., Eckert, C.: A comparative study of real-valued negative selection to statistical anomaly detection techniques. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 262–275. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Watkins, A., Boggess, L.: A new classifier based on resource limited artificial immune systems. In: Proceedings of the 2002 Congress on Evolutionary Computation CEC 2002, pp. 1546–1551. IEEE Press, Los Alamitos (2002)CrossRefGoogle Scholar
  8. 8.
    Bezerra, G.B., Barra, T.V., de Castro, L.N., Von Zuben, F.J.: Adaptive radius immune algorithm for data clustering. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 290–303. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Bentley, P.J., Greensmith, J., Ujjin, S.: Two ways to grow tissue for artificial immune systems. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 139–152. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Hart, E., Ross, P.: Studies on the implications of shape-space models for idiotypic networks. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 413–426. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Leppmeier, M.: Kugelpackungen von Kepler bis heute. Vieweg Verlag (1997)Google Scholar
  12. 12.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
  13. 13.
    Bellman, R.: Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton (1961)MATHGoogle Scholar
  14. 14.
    Mosegaard, K., Sambridge, M.: Monte Carlo analysis of inverse problems. Inverse problems 18, 29–54 (2002)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Fishman, G.S.: Monte Carlo Concepts, Algorithms, and Applications. Springer, Heidelberg (1995)Google Scholar
  16. 16.
    Stibor, T., Mohr, P.H., Timmis, J., Eckert, C.: Is negative selection appropriate for anomaly detection? In: Proceedings of Genetic and Evolutionary Computation Conference – GECCO-2005, pp. 321–328. ACM Press, New York (2005)CrossRefGoogle Scholar
  17. 17.
    Hettich, S., Bay, S.D.: KDD Cup 1999 Data (1999), http://kdd.ics.uci.edu
  18. 18.
    Verleysen, M.: Learning high-dimensional data. Limitations and Future Trends in Neural Computation 186, 141–162 (2003)Google Scholar
  19. 19.
    Vapnik, V.N.: The Nature of Statistical Learning Theory, 2nd edn. Springer, Heidelberg (1999)Google Scholar
  20. 20.
    Schölkopf, B., Platt, J.C., Shawe-Taylor, Smola, A.J., Williamson, R.C.: Estimating the support of a high-dimensional distribution. Technical Report MSR-TR-99-87, Microsoft Research (MSR) (1999)Google Scholar
  21. 21.
    Freitas, A., Timmis, J.: Revisiting the Foundations of Artificial Immune Systems: A Problem Oriented Perspective. In: Timmis, J., Bentley, P.J., Hart, E. (eds.) ICARIS 2003. LNCS, vol. 2787, pp. 229–241. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thomas Stibor
    • 1
  • Jonathan Timmis
    • 2
  • Claudia Eckert
    • 1
  1. 1.Department of Computer ScienceDarmstadt University of Technology 
  2. 2.Departments of Electronics and Computer ScienceUniversity of YorkHeslington

Personalised recommendations