Skip to main content
Log in

Multi-objective cost-sensitive attribute reduction on data with error ranges

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In current supervised machine learning research spectrum, there are several attribute reduction methodologies to acquire reducts with low test cost. They can deal with symbolic data, or numeric data with error ranges. In many cases, they consider the situation with only one type of cost; therefore the problem is single-objective. This paper addresses the attribute reduction problem on data with multi-type-costs and error ranges. First, we define the multi-objective attribute reduction problem where multi-type-costs are involved. Second, we propose three metrics to evaluate the quality of a reduct set. Third, we design a backtrack algorithm to compute the Pareto optimal set, and a heuristic algorithm to find a sub-optimal reduct set. Finally, we compare these algorithms on seven UCI (University of California-Irvine) datasets. Experimental results indicate that our heuristic algorithm has good capability of tackling the proposed problem.

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.

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

Similar content being viewed by others

References

  1. Du Y, Hu Q, Zhu P, Ma P (2011) Rule learning for classification based on neighborhood covering reduction. Inf Sci 181(24):5457–5467

    Article  MathSciNet  Google Scholar 

  2. Greiner R, Grove A, Roth D (2002) Learning cost-sensitive active classifiers. Artif Intell J 139(2):137–174

    Article  MathSciNet  Google Scholar 

  3. Hu Q, Yu D, Liu J, Wu C (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594

    Article  MathSciNet  MATH  Google Scholar 

  4. Hunt EB, Marin J, Stone PJ (1966) Experiments in induction. Academic Press, New York. ISBN:0123623502, 978-0123623508

  5. John GH, Langley P (1995) Estimating continuous distributions in Bayesian classifiers. In: Proceedings of the eleventh conference on uncertainty in artificial intelligence. Morgan Kaufmann, San Mateo, pp 338–345

  6. Kukar M, Kononenko I (1998) Cost-sensitive learning with neural networks. In: Proceedings of the 13th european conference on artificial intelligence. pp 445–449

  7. Li JK, Zhao H, Zhu W (2014) Fast randomized algorithm with restart strategy for minimal test cost feature selection. Int J Mach Learn Cybern 5(3):234–556

    Google Scholar 

  8. Li L, Chen H, Zhu W (2012) Attribute reduction in time–cost-sensitive decision systems through backtracking

  9. Li XJ, Zhao H, Zhu W (2014) An exponent weighted algorithm for the minimal cost feature selection. Int J Mach Learn Cybern. doi:10.1007/s13042-014-0279-4

  10. Liu J, Liao S, Min F, Zhu W (2013) Test cost constraint attribute reduction through a genetic approach. J Inf Comput Sci 10(3):839–849

    Google Scholar 

  11. Min F, He H, Qiao Y, Zhu W (2011) Test-cost-sensitive attribute reduction. Inf Sci 181:4928–4942

    Article  Google Scholar 

  12. Min F, Liu QH (2009) A hierarchical model for test-cost-sensitive decision systems. Inf Sci 179(14):2442–2452

    Article  MathSciNet  MATH  Google Scholar 

  13. Min F, Zhu W (2012) Attribute reduction of data with error ranges and test cost. Inf Sci 211(30):48–67

    Article  MathSciNet  MATH  Google Scholar 

  14. Pawlak Z (1982) Rough sets. Int J Parallel Progr 11(5):341–356

    MathSciNet  MATH  Google Scholar 

  15. Quinlan J (1986) Induction of decision trees. Mach Learn 1:81–106

  16. Quinlan J (1993) C4.5: programs for machine learning. Morgan Kaufmann, Los Altos

  17. Salvatore G, Benedetto M, Roman S (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47

    Article  MATH  Google Scholar 

  18. Sun L, Xu J, Tian Y (2012) Feature selection using rough entropy-based uncertainty measures in incomplete decision systems. Knowl-based Syst 36:206–216

  19. Turney P (1995) Cost-sensitive classification: empirical evaluation of a hybrid genetic decision tree induction algorithm. J Artif Intell Res 2:369–409

    Google Scholar 

  20. Turney P (2000) Types of cost in inductive concept learning. In: Workshop on cost-sensitive learning at the 17th international conference on machine learning. Stanford University, California

  21. Wang G, Du H, Yang D (2002) Reduction of decision table based on condition information entropy. Chin J Comput 25(7):759–766

    Google Scholar 

  22. Wong S, Ziarko W (1985) Optimal decision rules in decision table. Bull Polish Acad Sci 33(11–12):693–696

    MathSciNet  MATH  Google Scholar 

  23. Xu B, Chen H, Zhu W (2013) Multi-objective cost-sensitive attribute reduction. In: 2013 IFSA world congress NAFIPS annual meeting Edmonton, Canada

  24. Xu B, Min F, Zhu W, Chen H (2014) A genetic algorithm to multi-objective cost-sensitive attribute reduction. J Comput Inf Syst 10(7):3011–3022

    Google Scholar 

  25. Yao YY (2004) A partition model of granular computing. In: Lecture notes in computer science, vol 3100. pp 232–253

  26. Zhao H, Min F, Zhu W (2013) Cost-sensitive feature selection of numeric data with measurement errors. J Appl Math 2013:1–13

    MATH  Google Scholar 

  27. Zhao H, Min F, Zhu W (2013) Test-cost-sensitive attribute reduction of data with normal distribution measurement errors. Math Prob Eng 2013:1–12. doi:10.1155/2013/946070

  28. Zhu W (2009) Relationship among basic concepts in covering-based rough sets. Inf Sci 17(14):2478–2486

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu W, Wang F (2003) Reduction and axiomization of covering generalized rough sets. Inf Sci 152(1):217–230

    Article  MathSciNet  MATH  Google Scholar 

  30. Zubek V, Dietterich T (2002) Pruning improves heuristic search for cost-sensitive learning. In: Proceedings of the 19th international conference on machine learning, Sydney, Australia. pp 27–34

Download references

Acknowledgments

This work is supported in part by the Natural Science Foundation of Sichuan Province Ministry of Education under Grant No. 11ZB018 and 12ZA292, National Science Foundation of China under Grant No. 61379089 and Scientific Research Startingproject of SWPU under Grant No. 2014QHZ025.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu Fang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, Y., Liu, ZH. & Min, F. Multi-objective cost-sensitive attribute reduction on data with error ranges. Int. J. Mach. Learn. & Cyber. 7, 783–793 (2016). https://doi.org/10.1007/s13042-014-0296-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-014-0296-3

Keywords

Navigation