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Adaptive Aspects of Combining Approximation Spaces

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Part of the book series: Cognitive Technologies ((COGTECH))

Summary

This chapter addresses issues concerning a problem of constructing an optimal classification algorithm. The notion of a parameterized approximation space is used to model the process of classifier construction. The process can be viewed as hierarchical searching for optimal information granulation to fit a concept described by empirical data. The problem of combining several parameterized information granules (given by classification algorithms) to obtain a global data description is described. Some solutions based on adaptive methods are presented.

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Reference

  1. Th. Bäck. An overview of parameter control methods by self-adaptation in evolutionary algorithms. Fundamenta Informaticae, 35(1): 51–66,1998.

    MATH  Google Scholar 

  2. S.D. Bay. Combining nearest neighbor classifiers through multiple feature subsets. In Proceedings of the 15th International Conference on Machine Learning (ICML’98), Morgan Kaufmann, San Mateo, CA, 1998.

    Google Scholar 

  3. J.G. Bazan, H.S. Nguyen, S.H. Nguyen, P. Synak, J. Wróblewski. Rough set algorithms in classification problem. In L. Polkowski, S. Tsumoto, and T.Y. Lin, editors, Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems, 49–88, Physica, Heidelberg, 2000.

    Chapter  Google Scholar 

  4. I. Düntsch, G. Gediga. Uncertainty measures of rough set prediction. Artificial Intelligence, 106: 77–107, 1998.

    Article  MathSciNet  Google Scholar 

  5. I. Düntsch, G. Gediga, H.S. Nguyen. Rough set data analysis in the KDD process. In Proceedings of the 8th International Conference on Information Processing and Management under Uncertainty (IPMU 2000), 220–226, Madrid, Spain, 2000.

    Google Scholar 

  6. I.T. Jolliffe. Principal Component Analysis. Springer, Berlin, 1986.

    Book  Google Scholar 

  7. M. Li, P. Vitanyi. An Introduction to Kolmogorov Complexity and its Applications. Springer, New York, 1993.

    MATH  Google Scholar 

  8. T.Y. Lin, A.M. Wildberger, editors. Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery. Simulation Councils, San Diego, CA, 1995.

    Google Scholar 

  9. H. Liu, H. Motoda, editors. Feature Extraction, Construction and Selection: A Data Mining Perspective. Kluwer, Dordrecht, 1998.

    Book  MATH  Google Scholar 

  10. S.H. Nguyen, L. Polkowski, A. Skowron, P. Synak, J. Wrblewski. Searching for approximate description of decision classes. In Proceedings of the 4th International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, (RSFD’96), 153–161, Tokyo, 1996.

    Google Scholar 

  11. H.S. Nguyen. Discretization of Real Value Attributes: Boolean Reasoning Approach. Ph.D. Dissertation, Faculty of Mathematics, Informatics and Mechanics, Warsaw University, 2002.

    Google Scholar 

  12. H.S. Nguyen, A.Skowron, J.Stepaniuk. Granular computing: A rough set approach. Computational Intelligence, 17(3): 514–544, 2001.

    Article  MathSciNet  Google Scholar 

  13. S.K. Pal, W. Pedrycz, A. Skowron, R. Swiniarski, editors. Rough-neuro computing (special issue). Vol. 36 of Neurocomputing: An International Journal, 2001.

    Google Scholar 

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

    MATH  Google Scholar 

  15. L. Polkowski, A. Skowron, J. Zytkow. Tolerance based rough sets. In [18], 55–58, 1994.

    Google Scholar 

  16. L. Polkowski, A. Skowron. Rough mereological foundations for design, analysis, synthesis and control in distributed systems. Information Sciences, 104(1/2): 129–156, 1998.

    MathSciNet  MATH  Google Scholar 

  17. L. Polkowski, A. Skowron, editors. Rough Sets in Knowledge Discovery Vols. 1, 2. Physica, Heidelberg, 1998.

    Book  Google Scholar 

  18. L. Polkowski, A. Skowron, editors. Rough-Neuro Computing. In Proceedings of the 2nd International Conference on Rough Sets and Current Trends in Computing (RSCTC 2000), LNAI 2005, 25–32, Springer, Heidelberg, 2001.

    Google Scholar 

  19. RSES homepage-rough set based data analysis system. Available at http://loic.mimuw.edu.plrrses/

  20. A. Skowron. Approximation spaces in rough neurocomputing. In S. Hirano, M. Inuiguchi, S. Tsumoto, editors, Rough Set Theory and Granular Computing, Physica, Heidelberg, to appear.

    Google Scholar 

  21. A. Skowron, J. Stepaniuk. Approximation of relations. In [38], 161–166, 1993.

    Google Scholar 

  22. A. Skowron, J. Stepaniuk. Generalized approximation spaces. In T.Y. Lin, A.M. Wild-berger, editors, Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery 18–21, Simulation Councils, San Diego, CA, 1995.

    Google Scholar 

  23. A. Skowron, J. Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27: 245–253, 1996.

    MathSciNet  MATH  Google Scholar 

  24. A. Skowron, J. Stepaniuk. Information granule decomposition. Fundamenta Informaticae, 47: 337–350, 2001.

    MathSciNet  MATH  Google Scholar 

  25. R. Slowiñski, D. Vanderpooten. Similarity Relation as a Basis for Rough Approximations. Report number 53/95 of the Institute of Computer Science, Warsaw University of Technology, 1995; see also P.P. Wang, editor, Advances in Machine Intelligence & Soft Computing, 17–33,Bookwrights,Raleigh,NC, 1997.

    Google Scholar 

  26. J. Stepaniuk. Approximation spaces, reducts and representatives. In L. Polkowski, A. Skowron, editors, Rough Sets in Knowledge Discovery, Vol. 2, 109–126, Physica, Heidelberg, 1998.

    Chapter  Google Scholar 

  27. J. Stepaniuk. Knowledge discovery by application of rough set methods. In L. Polkowski, T.Y. Lin, S. Tsumoto, editors, Rough Sets: New Developments in Knowledge Discovery in Information Systems, Physica, Heidelberg, 2000.

    Google Scholar 

  28. D. Ślęzak. Approximate reducts in decision tables. In Proceedings of the 7th International Conference on Information Processing and Management under Uncertainty (IPMU’96), 1159–1164, Universidad da Granada, Granada, 1996.

    Google Scholar 

  29. D. Ślęzak, J.Wróblewski. Classification algorithms based on linear combinations of features. In Proceedings of the 3rd European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD’99), LNAI 1704, 548–553, Springer, Berlin, 1999.

    Google Scholar 

  30. D. Ślęzak, J. Wróblewski. Application of normalized decision measures to the new case classification. In Proceedings of the 2nd International Conference on Rough Sets and Current Trends in Computing (RSCTC 2000), LNAI 2005, 515–522, Springer, Berlin, 2000.

    Google Scholar 

  31. D. Ślęzak. Approximate Decision Reducts. Ph.D. Dissertation, Faculty of Mathematics, Informatics and Mechanics, Warsaw University, 2002 (in Polish).

    Google Scholar 

  32. P. Stone. Layered Learning in Multi-Agent Systems: A Winning Approach to Robotic Soccer. MIT Press, Cambridge, MA, 2000.

    Google Scholar 

  33. J. Wróblewski. Analyzing relational databases using rough set based methods. In Proceedings of the 8th Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2000), 256–262, Madrid, Spain, 2000.

    Google Scholar 

  34. J.Wróblewski. Ensembles of classifiers based on approximate reducts. In Proceedings of the Workshop on Concurrency, Specification and Programming (CS&P 2000), volume 140(2) of Informatik-Bericht, 355–362, Humboldt-Universität, Berlin, 2000; also in Fundamenta Informaticae, 47(3/4): 351–360, 2001.

    MATH  Google Scholar 

  35. J. Wróblewski. Adaptive Methods of Object Classification. Ph.D. Dissertation, Faculty of Mathematics, Informatics and Mechanics, Warsaw University, 2002 (in Polish).

    Google Scholar 

  36. L.A. Zadeh, J.Kacprzyk, editors. Computing with Words in Information/Intelligent Systems, Vols. 1, 2. Physica, Heidelberg, 1999.

    Book  Google Scholar 

  37. W. Ziarko. Variable precision rough set model. Journal of Computer and System Sciences, 46: 39–59, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  38. W. Ziarko, editor.Proceedings of the International Workshop on Rough Sets, Fuzzy Sets and Knowledge Discovery (RSKD’93),Workshops in Computing,Springer & British Computer Society, London, Berlin,1994.

    Book  Google Scholar 

  39. W. Ziarko. Approximation region-based decision tables. In Proceedings of the 1st International Conference on Rough Sets and Current Trends in Computing (RSCTC’98), LNAI 1424, 178–185, Springer, Berlin, 1998.

    Google Scholar 

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Wróblewski, J. (2004). Adaptive Aspects of Combining Approximation Spaces. In: Pal, S.K., Polkowski, L., Skowron, A. (eds) Rough-Neural Computing. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18859-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-18859-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62328-8

  • Online ISBN: 978-3-642-18859-6

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