Skip to main content

A New Classifier Based on the Dual Indiscernibility Matrix

  • Conference paper
  • First Online:
Information and Software Technologies (ICIST 2016)

Abstract

A new approach to classifier synthesis was proposed by Polkowski and in this work we propose an implementation of this idea. The idea is based on usage of a dual indiscernibility matrix which allows to determine for each test object in the data, pairs of training objects which cover in a sense the given test object. A family of pairs best covering the given object pass their decisions for majority voting on decision for the test object. We present results obtained by our classifier on standard data from UCI Repository and compare them with results obtained by means of k-NN and Bayes classifiers. The results are validated by multiple cross-validation. We find our classifier on par with k-NN and Bayes classifiers.

In this work Sect. 1, Introduction, gives basic definitions of the notions applied and proposed method, Sect. 2 brings forth results of experiments with real data from UCI Repository. The last Sect. 3 is devoted to a discussion of results and concluding remarks.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Polkowski, L.T., Nowak, B.A.: Betweeness, Lukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper–Granules, Conflict Resolution. IOS Press, Fundamenta Informaticae XX (2016) (forthcoming)

    Google Scholar 

  2. Starczewski, J., Nowicki, R.K., Nowak, B.A.: Genetic fuzzy classifier with fuzzy rough sets for imprecise data. In: 2014 IEEE International Conference on Fuzzy Systems, pp. 1382–1389 (2014)

    Google Scholar 

  3. Devroye, L., Gyorfi, L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition. Springer, New York (1996)

    Book  MATH  Google Scholar 

  4. Grzymala-Busse, J.W.: LERS - a system for learning from examples based on rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer, Dordrecht (1992)

    Google Scholar 

  5. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    Book  MATH  Google Scholar 

  7. Pawlak, Z.: An inquiry into anatomy of conflicts. J. Inform. Sci. 109, 65–78 (1998)

    Article  MathSciNet  Google Scholar 

  8. Pawlak, Z., Skowron, A.: A rough set approach for decision rules generation. In: Proceedings of IJCAI 1993 Workshop W12 (1993)

    Google Scholar 

  9. Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approximate Reasoning 15(4), 333–365 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  10. UCI Repository. http://www.ics.uci.edu/mlearn/databases

  11. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems, intelligent decision support. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory. Theory and Decision Library, vol. 11, pp. 331–362. Springer, Dordrecht (1992)

    Chapter  Google Scholar 

  12. Polkowski, L.: Betweenness, lukasiewicz rough inclusions, euclidean representations in information systems, hyper-granules, conflict resolution. In: Proceedings of the 24th International Workshop on Concurrency, Specification and Programming, pp 97–110. University of Rzeszow (2015). http://ceur-ws.org/Vol-1492/

  13. Polkowski, L., Artiemjew, P.: Granular Computing in Decision Approximation: An Application of Rough Mereology. Intelligent Systems Reference Library, vol. 77. Springer, Heidelberg (2015)

    MATH  Google Scholar 

  14. Polkowski, L.: Rough Sets: Mathematical Foundations. Advances in Intelligent and Soft Computing. Springer/Physica-Verlag, Heidelberg (2002)

    Book  MATH  Google Scholar 

  15. Nowak, B.A., Nowicki, R.K., Woźniak, M., Napoli, C.: Multi-class nearest neighbour classifier for incomplete data handling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.). LNCS, vol. 9119, pp. 469–480. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  16. Woźniak, M., Marszałek, Z., Gabryel, M., Nowicki, R.K.: Modified merge sort algorithm for large scale data sets. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 612–622. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Korytkowski, M., Nowicki, R., Rutkowski, L., Scherer, R.: AdaBoost ensemble of DCOG rough–neuro–fuzzy systems. In: Jędrzejowicz, P., Nguyen, N.T., Hoang, K. (eds.) ICCCI 2011, Part I. LNCS, vol. 6922, pp. 62–71. Springer, Heidelberg (2011)

    Google Scholar 

  18. Zalasiński, M., Cpałka, K.: New algorithm for on-line signature verification using characteristic hybrid partitions. In: Wilimowska, Z., Borzemski, L., Grzech, A., Świątek, J. (eds.) Information Systems Architecture and Technology: Proceedings of 36th International Conference on Information Systems Architecture and Technology – ISAT 2015 – Part IV. Advances in Intelligent Systems and Computing, vol. 432, pp. 147–157. Springer, Heidelberg (2016)

    Google Scholar 

  19. Drozda, P., Sopyła, K., Górecki, P.: Different orderings and visual sequence alignment algorithms for image classification. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 693–702. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

Download references

Acknowledgement

The research has been supported by grant 1309-802 from Ministry of Science and Higher Education of the Republic of Poland.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bartosz A. Nowak .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Artiemjew, P., Nowak, B.A., Polkowski, L.T. (2016). A New Classifier Based on the Dual Indiscernibility Matrix. In: Dregvaite, G., Damasevicius, R. (eds) Information and Software Technologies. ICIST 2016. Communications in Computer and Information Science, vol 639. Springer, Cham. https://doi.org/10.1007/978-3-319-46254-7_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46254-7_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46253-0

  • Online ISBN: 978-3-319-46254-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics