Skip to main content
SpringerLink
Log in

Greedy Algorithm for the Construction of Approximate Decision Rules for Decision Tables with Many-Valued Decisions

  • Chapter
  • First Online:
Transactions on Rough Sets XX

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 10020))

Abstract

The paper is devoted to the study of a greedy algorithm for construction of approximate decision rules. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. We consider bounds on the precision of this algorithm relative to the length of rules. To illustrate proposed approach we study a problem of recognition of labels of points in the plain. This paper contains also results of experiments with modified decision tables from UCI Machine Learning Repository.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Alkhalid, A., Amin, T., Chikalov, I., Hussain, S., Moshkov, M., Zielosko, B.: Dagger: a tool for analysis and optimization of decision trees andrules. Comput. Inf. Soc. Factors New Inf. Technol. Hypermedia Perspect. Avant-Garde Experiences Eraof Communicability Expansion, 29–39 (2011)

    Google Scholar 

  2. Azad, M., Chikalov, I., Moshkov, M., Zielosko, B.: Greedy algorithms for construction of approximate tests for decision tables with many-valued decisions. Fundamenta Informaticae 120(3–4), 231–242 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Blockeel, H., Schietgat, L., Struyf, J., Džeroski, S., Clare, A.: Decision trees for hierarchical multilabel classification: a case study in functional genomics. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 18–29. Springer, Heidelberg (2006). doi:10.1007/11871637_7

    Chapter  Google Scholar 

  4. Boutell, M.R., Luo, J., Shen, X., Brown, C.M.: Learning multi-label scene classification. Pattern Recogn. 37(9), 1757–1771 (2004)

    Article  Google Scholar 

  5. Cheriyan, J., Ravi, R.: Lecture notes on approximation algorithms for network problems (1998). http://www.math.uwaterloo.ca/~jcheriya/lecnotes.html

  6. Chikalov, I., Zielosko, B.: Decision rules for decision tables with many-valued decisions. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS (LNAI), vol. 6954, pp. 763–768. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24425-4_95

    Chapter  Google Scholar 

  7. Clare, A., King, R.D.: Knowledge discovery in multi-label phenotype data. In: Raedt, L., Siebes, A. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 42–53. Springer, Heidelberg (2001). doi:10.1007/3-540-44794-6_4

    Chapter  Google Scholar 

  8. Comité, F., Gilleron, R., Tommasi, M.: Learning multi-label alternating decision trees from texts and data. In: Perner, P., Rosenfeld, A. (eds.) MLDM 2003. LNCS, vol. 2734, pp. 35–49. Springer, Heidelberg (2003). doi:10.1007/3-540-45065-3_4

    Chapter  Google Scholar 

  9. Feige, U.: A threshold of ln n for approximating set cover. J. ACM (JACM) 45(4), 634–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)

    Article  MATH  Google Scholar 

  11. Kryszkiewicz, M.: Rules in incomplete information systems. Inf. Sci. 113(34), 271–292 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lichman, M.: UCI Machine Learning Repository (2013)

    Google Scholar 

  13. Lipski, W.: On databases with incomplete information. J. ACM (JACM) 28(1), 41–70 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lipski Jr., W.: On semantic issues connected with incomplete information databases. ACM Trans. Database Syst. 4(3), 262–296 (1979)

    Article  Google Scholar 

  15. Mencia, E.L., Furnkranz, J.: Pairwise learning of multilabel classifications with perceptrons. In: IEEE International Joint Conference on Neural Networks, 2008, IJCNN 2008 (IEEE World Congress on Computational Intelligence), pp. 2899–2906 (2008)

    Google Scholar 

  16. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: Partial Covers, Reducts and Decision Rules in Rough Sets–Theory and Applications. SCI, vol. 145. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  17. Moshkov, M., Zielosko, B.: Combinatorial Machine Learning–A Rough Set Approach. SCI, vol. 360. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  18. Moshkov, M., Zielosko, B.: Construction of \(\alpha \)-decision trees for tables with many-valued decisions. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS (LNAI), vol. 6954, pp. 486–494. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24425-4_63

    Chapter  Google Scholar 

  19. Moshkov, M.J.: Greedy algorithm for decision tree construction in context of knowledge discovery problems. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 192–197. Springer, Heidelberg (2004). doi:10.1007/978-3-540-25929-9_22

    Chapter  Google Scholar 

  20. Nguyen, H.S., Slezak, D.: Approximate reducts and association rules - correspondence and complexity results. In: Proceedings of the 7th International Workshop on New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. RSFDGrC 1999, pp. 137–145. Springer, London (1999)

    Google Scholar 

  21. Orowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoret. Comput. Sci. 29(12), 27–39 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  23. Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Inf. Sci. 177(1), 41–73 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177(1), 28–40 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)

    Article  MATH  Google Scholar 

  27. Sakai, H., Ishibashi, R., Koba, K., Nakata, M.: Rules and apriori algorithm in non-deterministic information systems. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 328–350. Springer, Heidelberg (2008). doi:10.1007/978-3-540-89876-4_18

    Chapter  Google Scholar 

  28. Sakai, H., Nakata, M., Ślȩzak, D.: Rule generation in lipski’s incomplete information databases. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS (LNAI), vol. 6086, pp. 376–385. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13529-3_40

    Chapter  Google Scholar 

  29. Sakai, H., Nakata, M., Ślęzak, D.: A prototype system for rule generation in lipski’s incomplete information databases. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds.) RSFDGrC 2011. LNCS (LNAI), vol. 6743, pp. 175–182. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21881-1_29

    Chapter  Google Scholar 

  30. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers (1992)

    Google Scholar 

  31. Ślȩzak, D.: Normalized decision functions and measures for inconsistent decision tables analysis. Fundamenta Informaticae 44(3), 291–319 (2000)

    MathSciNet  MATH  Google Scholar 

  32. Ślȩzak, D.: Approximate entropy reducts. Fundamenta Informaticae 53(3–4), 365–390 (2002)

    MathSciNet  MATH  Google Scholar 

  33. Tsoumakas, G., Katakis, I.: Multi-label classification: an overview. Int. J. Data Warehouse. Min. 3(3), 1–13 (2007)

    Article  Google Scholar 

  34. Tsoumakas, G., Katakis, I., Vlahavas, I.: Mining multi-label data. In: Data Mining and Knowledge Discovery Handbook, pp. 667–685. Springer, US (2010)

    Google Scholar 

  35. Wieczorkowska, A., Synak, P., Lewis, R., Raś, Z.W.: Extracting emotions from music data. In: Hacid, M.-S., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds.) ISMIS 2005. LNCS (LNAI), vol. 3488, pp. 456–465. Springer, Heidelberg (2005). doi:10.1007/11425274_47

    Chapter  Google Scholar 

  36. Zhou, Z.H., Jiang, K., Li, M.: Multi-instance learning based web mining. Appl. Intell. 22(2), 135–147 (2005)

    Article  Google Scholar 

  37. Zhou, Z.H., Zhang, M.L., Huang, S.J., Li, Y.F.: Multi-instance multi-label learning. Artif. Intell. 176(1), 2291–2320 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST).

The authors wish to express their gratitude to anonymous reviewers for useful comments.

Author information

Authors and Affiliations

  1. Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Mohammad Azad & Mikhail Moshkov

  2. Institute of Computer Science, University of Silesia, 39, Bȩdzińska St., 41-200, Sosnowiec, Poland

    Beata Zielosko

Authors
  1. Mohammad Azad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikhail Moshkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Beata Zielosko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Azad .

Editor information

Editors and Affiliations

  1. University of Manitoba , Winnipeg, Manitoba, Canada

    James F. Peters

  2. University of Warsaw , Warsaw, Poland

    Andrzej Skowron

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag GmbH Germany

About this chapter

Cite this chapter

Azad, M., Moshkov, M., Zielosko, B. (2016). Greedy Algorithm for the Construction of Approximate Decision Rules for Decision Tables with Many-Valued Decisions. In: Peters, J., Skowron, A. (eds) Transactions on Rough Sets XX. Lecture Notes in Computer Science(), vol 10020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53611-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53611-7_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53610-0

  • Online ISBN: 978-3-662-53611-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation