Abstract
Two probabilistic approaches to rough sets are discussed in this chapter: the variable precision rough set model and the Bayesian rough set model, as they apply to data dependencies detection, analysis and their representation. The focus is on the analysis of data co-occurrence-based dependencies appearing in classification tables and probabilistic decision tables acquired from data. In particular, the notion of attribute reduct, in the framework of probabilistic approach, is of interest in the chapter. The reduct allows for information-preserving elimination of redundant attributes from classification tables and probabilistic decision tables. The chapter includes two efficient reduct computation algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bac, L., Tuan, N.: Using rough set in feature selection and reduction in face recognition problem. In: Proceedings of the 9th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining PAKDD. Lecture Notes in Artificial Intelligence, vol. 3518, pp. 226–233 (2005)
Beynon, M.: Reducts within the variable precision rough sets model: a further investigation. Eur. J. Oper. Res. 134(3), 592–605 (2001)
Beynon, M., Peel, M.: Variable precision rough set theory and data discretization: an application to corporate failure prediction. Int. J. Manag. Sci. 29, 561–576 (2001)
Chen, X., Ziarko, W.: Rough set-based incremental learning approach to face recognition. In: Proceedings of the International Conference on Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence, vol. 6086, pp. 356–365 (2010)
Greco, S., Matarazzo, B., Slowinski, R.: Multicriteria classification by dominance-based rough set approach. In: Kloesgen, W., Zytkow, J. (eds.) Handbook of Data Mining and Knowledge Discovery, chap. C5.1.9. Oxford University Press, New York (2002)
Inuiguchi, M., Yoshioka, Y., Kusunoki, Y.: Variable-precision dominance-based rough set approach and attribute reduction. Int. J. Approx. Reason. 50, 1199–1214 (2009)
Katzberg, J., Ziarko, W.: Variable precision rough sets with asymmetric bounds. In: Ziarko, W. (ed.) Proceedings of the International Workshop on Rough Sets, Fuzzy Sets and Knowledge Discovery RSKD, pp. 167–177. Springer, London (1994)
Mi, J., Leung, Y., Wu, W.: Approaches to attribute reduction in concepts lattices induced by axialities. Knowl. Based Syst. 23(6), 504–511 (2010)
Nguyen, H.: On exploring soft discretization of continuous attributes. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies, pp. 333–350. Springer (2003)
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, The Netherlands (1991)
Peters, J.F., Ramanna, S.: Feature selection: near set approach. In: Proceedings of the 3rd ECML/PKDD International Workshop on Mining Complex Data MCD, pp. 57–71 (2007)
Slezak, D., Ziarko, W.: Attribute reduction in the Bayesian version of variable precision rough set model. Electron. Notes Theor. Comput. Sci. 82(4), 263–273 (2003)
Swiniarski, R., Skowron, A.: Rough set methods in feature selection and recognition. Pattern Recognit. Lett. 24(6), 833–849 (2003)
Wei, L., Zhang, W.: Probabilistic rough sets characterized by fuzzy sets. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 12, 47–60 (2004)
Xia Wang, X., Zhang, W.: Relations of attribute reduction between object and property oriented concept lattices. Knowl. Based Syst. 21(5), 398–403 (2008)
Yao, Y.: Decision theoretic rough set models, rough sets and knowledge. In: Proceedings of of the 2nd International Conference on Rough Sets and Knowledge Technology RSKT. Lecture Notes in Artificial Intelligence, vol. 4481, pp. 1–12 (2007)
Yao, Y., Lin, T.: Generalization of rough sets using modal logic. Intell. Autom. Soft Comput. 2(2), 103–120 (1996)
Yao, Y., Zhao, Y.: Discernibility matrix simplification for constructing attribute reducts. Inf. Sci. 179(5), 867–882 (2009)
Yao, Y., Zhao, Y., Wang, J.: On reduct construction algorithms. In: Proceedings of the 1st International Conference on Rough Sets and Knowledge Technology RSKT. Lecture Notes in Artificial Intelligence, vol. 4062, pp. 297–304 (2006)
Zhang, W., Mi, J., Wu, W.: Approaches to knowledge reductions in inconsistent systems. Int. J. Intell. Syst. 18(9), 989–1000 (2003)
Zhang, H., Leung, Y., Zhou, L.: Variable precision-dominance based rough set approach to interval-valued information systems. Inf. Sci. 244, 75–272 (2013)
Zhang, J., Wang, J., Li, D., He, H., Sun, J.: A new heuristic reduct algorithm based on rough sets theory. In: Proceedings of the 4th International Conference on Advances in Web-Age Information Management WAIM. Lecture Notes on Computer Science, vol. 2762, pp. 247–253 (2003)
Zhao, Y., Luo, F., Wong, S., Yao, Y.: A general definition of an attribute reduct. In: Proceedings of the 2nd International Conference on Rough Sets and Knowledge Technology RSKT, Lecture Notes in Artificial Intelligence, vol. 4481, pp. 101–108 (2007)
Zhong, N., Dong, J.: Using rough sets with heuristics for feature selection. J. Intell. Inf. Syst. 16, 199–214 (2001)
Ziarko, W.: Variable precision rough sets model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)
Ziarko, W.: Decision making with probabilistic decision tables. In: Proceedings of the 7th International Workshop on Rough Sets. Fuzzy Sets, Data Mining and Granular Computing RSFDGrC. Lecture Notes on Artificial Intelligence, pp. 463–471. Springer, Yamaguchi (1999)
Ziarko, W.: Probabilistic decision tables in the variable precision rough set model. Comput. Intell. 17(3), 593–603 (2002)
Ziarko, W.: Rough set approaches for discovery of rules and attribute dependencies. In: Kloesgen, W., Zytkow, J. (eds.) Handbook of Data Mining and Knowledge Discovery, pp. 328–339. Oxford University Press, New York (2002)
Ziarko, W.: Set approximation quality measures in the variable precision rough set model. In: Proceedings of the 2nd International Conference on Hybrid Intelligent Systems HIS. Soft Computing Systems, Management and Applications, vol. 87, pp. 442–452. IOS Press (2002)
Ziarko, W.: Acquisition of hierarchy—structured probabilistic decision tables, and rules from data. Expert Syst., Int. J. Knowl. Eng. Neural Netw. 20(5), 10–305 (2003)
Ziarko, W.: Probabilistic rough sets. In: Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing RSFDGrC. Lecture Notes in Computer Science, vol. 3641, pp. 283–293 (2005)
Ziarko, W.: Partition dependencies in hierarchies of probabilistic decision tables. In: Proceedings of the 1st International Conference on Rough Sets and Knowledge Technology RSKT. Lecture Notes in Artificial Intelligence, vol. 4062, pp. 42–49 (2006)
Ziarko, W.: Probabilistic approach to rough sets. Int. J. Approx. Reason. 49(2), 272–284 (2008)
Ziarko, W.: Probabilistic Dependencies in Linear Hiearchies of Decision Tables. Transactions on Rough Sets 9, vol. 5390, pp. 444–454 (2008)
Acknowledgments
Thanks are due to anonymous referees for their detailed and inspiring comments. The research reported in the chapter was supported by research grants from Natural Sciences and Engineering Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ziarko, W. (2015). Dependency Analysis and Attribute Reduction in the Probabilistic Approach to Rough Sets. In: Stańczyk, U., Jain, L. (eds) Feature Selection for Data and Pattern Recognition. Studies in Computational Intelligence, vol 584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45620-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-45620-0_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45619-4
Online ISBN: 978-3-662-45620-0
eBook Packages: EngineeringEngineering (R0)