Skip to main content

Advertisement

Log in

Learning cellular automata rules for binary classification problem

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

This paper proposes a cellular automata-based solution of a binary classification problem. The proposed method is based on a two-dimensional, three-state cellular automaton (CA) with the von Neumann neighborhood. Since the number of possible CA rules (potential CA-based classifiers) is huge, searching efficient rules is conducted with use of a genetic algorithm (GA). Experiments show an excellent performance of discovered rules in solving the classification problem. The best found rules perform better than the heuristic CA rule designed by a human and also better than one of the most widely used statistical method: the k-nearest neighbors algorithm (k-NN). Experiments show that CAs rules can be successfully reused in the process of searching new rules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Algorithm 1
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Bailey T, Jain A (1978) A note on distance-weighted k-nearest neighbor rules. IEEE Trans Syst Man Cybern 8(4):311–313

    Article  MATH  Google Scholar 

  2. Breukelaar R, Back T (2004) Evolving transition rules for multi dimensional cellular automata. In: Lecture notes in computer science, vol 3305. Springer, Berlin, pp 182–191

    Google Scholar 

  3. Das R, Crutchfield J, Mitchell M (1995) Evolving globally synchronized cellular automata. In: Proceedings of the 6th international conference on genetic algorithms, pp 336–343

    Google Scholar 

  4. Fawcett T (2008) Data mining with cellular automata. ACM SIGKDD Explor Newsl 10(1):32–39

    Article  Google Scholar 

  5. Gacs P, Kurdyumov G, Levin L (1978) One dimensional uniform arrays that wash out finite islands. Probl Pereda Inf 12:92–98

    Google Scholar 

  6. Ishibuchi H, Nozaki K, Yamamoto N (1993) Selecting fuzzy rules by genetic algorithm for classification problems. Fuzzy Sets Syst 2:1119–1124

    Google Scholar 

  7. Maji P, Sikdar B, Chaudhuri P (2004) Cellular automata evolution for pattern classification. In: Lecture notes in computer science, vol 3305. Springer, Berlin, pp 660–669

    Google Scholar 

  8. Mitchell M, Hraber P, Crutchfield J (1993) Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Syst 7:89–130

    MATH  Google Scholar 

  9. Oliveira C Jr., de Oliveira P (2008) An approach to searching for two-dimensional cellular automata for recognition of handwritten digits. In: Lecture notes in artificial intelligence, vol 5317. Springer, Berlin, pp 462–471

    Google Scholar 

  10. Omohundro S (1984) Modelling cellular automata with partial differential equations. Physica 10D, 10(1–2):128–134

    MathSciNet  Google Scholar 

  11. Piwonska A, Seredynski F (2010) Learning cellular automata rules for pattern reconstruction task. In: Lecture notes in computer science, vol 6457. Springer, Berlin, pp 240–249

    Google Scholar 

  12. Povalej P, Lenic M, Kokol P (2004) Improving ensembles with classificational cellular automata. In: Lecture notes in computer science, vol 3305. Springer, Berlin, pp 242–249

    Google Scholar 

  13. Sipper M (1997) The evolution of parallel cellular machines toward evolware. Biosystems 42(1):29–43

    Article  Google Scholar 

  14. Wolfram S (2002) A new kind of science. Wolfram Media, Champain

    MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by the grant S/WI/2/2008 from Bialystok University of Technology.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miroslaw Szaban.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Piwonska, A., Seredynski, F. & Szaban, M. Learning cellular automata rules for binary classification problem. J Supercomput 63, 800–815 (2013). https://doi.org/10.1007/s11227-012-0767-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-012-0767-9

Keywords

Navigation