Using Positive Region to Reduce the Computational Complexity of Discernibility Matrix Method
Rough set discernibility matrix method is a valid method to attribute reduction. However, it is a NP-hard problem. Up until now, though some methods have been proposed to improve this problem, the case is not improved well. We find that the idea of discernibility matrix can be used to not only the whole data but also partial data. So we present a new algorithm to reduce the computational complexity. Firstly, select a condition attribute C that holds the largest measure of γ(C, D) in which the decision attribute D depends on C. Secondly, with the examples in the non-positive region, build a discernibility matrix to create attribute reduction. Thirdly, combine the attributes generated in the above two steps into the attribute reduction set. Additionally, we give a proof of the rationality of our method. The larger the positive region is; the more the complexity is reduced. Four Experimental results indicate that the computational complexity is reduced by 67%, 83%, 41%, and 30% respectively and the reduced attribute sets are the same as the standard discernibility matrix method.
KeywordsDecision Attribute Disjunctive Normal Form Forest Cover Type Discernibility Matrix Chinese Character Recognition
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- 2.Wong, S.K., Ziarko, W.: On optimal decision rules in decision tables. Bulletin of Polish Academy of Sciences 33, 357–362 (1985)Google Scholar
- 5.HTWroblewski, J.T.: T Ensembles of classifiers based on approximate reducts. In: Fundamenta Informaticae, vol. 47, pp. 351–360. IOS Press, Netherlands (2001)Google Scholar
- 6.HWroblewski, J.H.: Covering with reducts-a fast algorithm for rule generaten. Rough Sets and Current Trends in Computing. In: Proceedings of First International Conference, RSCTC 1998, pp. 402–407 (1998)Google Scholar
- 7.HXiao, J.-M.: New rough set approach to knowledge reduction in decision table. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2208–2211 (2004)Google Scholar
- 8.Jin-song, F., Ting-jian, F.: Rough set and SVM based pattern classification method. Pattern Recognition and Artificial Intelligence 13, 419–423 (2000)Google Scholar