Nature Inspired Population-Based Heuristics for Rough Set Reduction

  • Hongbo Liu
  • Ajith Abraham
  • Yanheng Li
Part of the Studies in Computational Intelligence book series (SCI, volume 174)


Finding reducts is one of the key problems in the increasing applications of rough set theory, which is also one of the bottlenecks of the rough set methodology. The population-based reduction approaches are attractive to find multiple reducts in the decision systems. In this chapter, we introduce two nature inspired population-based computational optimization techniques, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) for rough set reduction. Particle Swarm Optimization (PSO) is particularly attractive for the challenging problem as a new heuristic algorithm. The approach discover the best feature combinations in an efficient way to observe the change of positive region as the particles proceed throughout the search space. We evaluated the performance of the two algorithms using some benchmark datasets and the corresponding computational experiments are discussed. Empirical results indicate that both methods are ideal for all the considered problems and particle swarm optimization technique outperformed the genetic algorithm approach by obtaining more number of reducts for the datasets. We also illustrate a real world application in fMRI data analysis, which is helpful for cognition research.


Particle Swarm Optimization Feature Selection Decision Table Particle Swarm Algorithm fMRI Data Analysis 
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.


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  1. 1.
    Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Pawlak, Z.: Rough Sets: Present State and The Future. Foundations of Computing and Decision Sciences 18, 157–166 (1993)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Pawlak, Z.: Rough Sets and Intelligent Data Analysis. Information Sciences 147, 1–12 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kusiak, A.: Rough Set Theory: A Data Mining Tool for Semiconductor Manufacturing. IEEE Transactions on Electronics Packaging Manufacturing 24, 44–50 (2001)CrossRefGoogle Scholar
  5. 5.
    Shang, C., Shen, Q.: Rough Feature Selection for Neural Network Based Image Classification. International Journal of Image and Graphics 2, 541–555 (2002)CrossRefGoogle Scholar
  6. 6.
    Francis, E.H., Tay, S.L.: Economic And Financial Prediction Using Rough Sets Model. European Journal of Operational Research 141, 641–659 (2002)zbMATHCrossRefGoogle Scholar
  7. 7.
    Świniarski, R.W., Skowron, A.: Rough Set Methods in Feature Selection and Recognition. Pattern Recognition Letters 24, 833–849 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Beaubouef, T., Ladner, R., Petry, F.: Rough Set Spatial Data Modeling for Data Mining. International Journal of Intelligent Systems 19, 567–584 (2004)zbMATHCrossRefGoogle Scholar
  9. 9.
    Shen, L., Francis, E.H.: Tay Applying Rough Sets to Market Timing Decisions. Decision Support Systems 37, 583–597 (2004)CrossRefGoogle Scholar
  10. 10.
    Gupta, K.M., Moore, P.G., Aha, D.W., Pal, S.K.: Rough set feature selection methods for case-based categorization of text documents. In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds.) PReMI 2005. LNCS, vol. 3776, pp. 792–798. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Boussouf, M.: A Hybrid Approach to Feature Selection. In: Żytkow, J.M. (ed.) PKDD 1998. LNCS, vol. 1510. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Świniarski, R.W. (ed.) Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  13. 13.
    Zhang, J., Wang, J., Li, D., He, H., Sun, J.: A new heuristic reduct algorithm base on rough sets theory. In: Dong, G., Tang, C., Wang, W. (eds.) WAIM 2003. LNCS, vol. 2762, pp. 247–253. Springer, Heidelberg (2003)Google Scholar
  14. 14.
    Hu, K., Diao, L., Shi, C.: A heuristic optimal reduct algorithm. In: Leung, K.-S., Chan, L., Meng, H. (eds.) IDEAL 2000. LNCS, vol. 1983, pp. 139–144. Springer, Heidelberg (2000)Google Scholar
  15. 15.
    Zhong, N., Dong, J.: Using Rough Sets with Heuristics for Feature Selection. Journal of Intelligent Information Systems 16, 199–214 (2001)zbMATHCrossRefGoogle Scholar
  16. 16.
    Banerjee, M., Mitra, S., Anand, A.: Feature Selection Using Rough Sets. Studies in Computational Intelligence 16, 3–20 (2006)CrossRefGoogle Scholar
  17. 17.
    Wu, Q., Bell, D.: Multi-knowledge Extraction and Application. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS, vol. 2639, pp. 574–575. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Wu, Q.: Multiknowledge and Computing Network Model for Decision Making and Localisation of Robots. Thesis, University of Ulster (2005)Google Scholar
  19. 19.
    Kennedy, J., Eberhart, R.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  20. 20.
    Clerc, M., Kennedy, J.: The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation 6, 58–73 (2002)CrossRefGoogle Scholar
  21. 21.
    Clerc, M.: Particle Swarm Optimization. ISTE Publishing Company, London (2006)zbMATHGoogle Scholar
  22. 22.
    Liu, H., Abraham, A., Clerc, M.: Chaotic Dynamic Characteristics in Swarm Intelligence. Applied Soft Computing Journal 7, 1019–1026 (2007)CrossRefGoogle Scholar
  23. 23.
    Parsopoulos, K.E., Vrahatis, M.N.: Recent approaches to global optimization problems through particle swarm optimization. Natural Computing 1, 235–306 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Abraham, A., Guo, H., Liu, H.: Swarm Intelligence: Foundations, Perspectives and Applications. In: Nedjah, N., Mourelle, L. (eds.) Swarm Intelligent Systems. Studies in Computational Intelligence, pp. 3–25. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Salman, A., Ahmad, I., Al-Madani, S.: Particle Swarm Optimization for Task Assignment Problem. Microprocessors and Microsystems 26, 363–371 (2002)CrossRefGoogle Scholar
  26. 26.
    Sousa, T., Silva, A., Neves, A.: Particle Swarm Based Data Mining Algorithms for Classification Tasks. Parallel Computing 30, 767–783 (2004)CrossRefGoogle Scholar
  27. 27.
    Liu, B., Wang, L., Jin, Y., Tang, F., Huang, D.: Improved Particle Swarm Optimization Combined With Chaos. Chaos, Solitons and Fractals 25, 1261–1271 (2005)zbMATHCrossRefGoogle Scholar
  28. 28.
    Schute, J.F., Groenwold, A.A.: A Study of Global Optimization Using Particle Swarms. Journal of Global Optimization 3, 108–193 (2005)Google Scholar
  29. 29.
    Liu, H., Abraham, A., Clerc, M.: An Hybrid Fuzzy Variable Neighborhood Particle Swarm Optimization Algorithm for Solving Quadratic Assignment Problems. Journal of Universal Computer Science 13(7), 1032–1054 (2007)Google Scholar
  30. 30.
    Wang, G.: Rough Reduction in Algebra View and Information View. International Journal of Intelligent Systems 18, 679–688 (2003)zbMATHCrossRefGoogle Scholar
  31. 31.
    Xu, Z., Liu, Z., Yang, B., Song, W.: A Quick Attibute Reduction Algorithm with Complexity of Max(O(|C||U|),O(|C|2|U/C|)). Chinese Journal of Computers 29, 391–399 (2006)Google Scholar
  32. 32.
    Wu, Q.X., Bell, D.A.: Multi-Knowledge Extraction and Application. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS, vol. 2639, pp. 274–279. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  33. 33.
    Cantú-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic publishers, Netherland (2000)zbMATHGoogle Scholar
  34. 34.
    Abraham, A.: Evolutionary Computation. In: Sydenham, P., Thorn, R. (eds.) Handbook for Measurement Systems Design, pp. 920–931. John Wiley and Sons Ltd., London (2005)Google Scholar
  35. 35.
    Arbib, M.A., Grethe, J.S. (eds.): Computing the Brain: A Guide to Neuroinformatics. Academic Press, London (2001)Google Scholar
  36. 36.
    Røed, G.: Knowledge Extraction from Process Data: A rough Set Approach to Data Mining on Time Series. Knowledge Extraction from Process data. Thesis, Norwegian University of Science and Technology (1999)Google Scholar
  37. 37.
    Ji, Y., Liu, H., Wang, X., Tang, Y.: Congitive States Classification from fMRI Data Using Support Vector Machines. In: Proceedings of The Third International Conference on Machine Learning and Cybernetics, pp. 2920–2923. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  38. 38.
    Goldberg, D.E.: Genetic Algorithms in search, optimization, and machine learning. Addison-Wesley Publishing Corporation, Inc., Reading (1989)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hongbo Liu
    • 1
  • Ajith Abraham
    • 2
  • Yanheng Li
    • 1
  1. 1.School of Computer Science and EngineeringDalian Maritime UniversityDalianChina
  2. 2.Centre for Quantifiable Quality of Service in Communication SystemsNorwegian University of Science and TechnologyTrondheimNorway

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