In order to solve the problem that weighted rough sets model lacks a mechanism to deal with mixed and imbalanced data
a unified fuzzy equivalent relationship for analyzing different types of features in weighted domain is established
and a weighted fuzzy rough sets model is proposed to deal with mixed data. Furthermore
a hybrid attribute-reduction algorithm is constructed based on the weighted fuzzy rough sets model. Compared with the classical crisp partition
the hybrid algorithm can avoid information loss through fuzzy soft partition generated by the model. Experimental results on imbalanced and mixed data sets show that the proposed weighted fuzzy rough sets model can not only select fewer features than weighted rough sets model
but also improve the average classification performance of the reduced attribute set on learning methods by 11.9%.
关键词
Keywords
references
PAWLAK Z, SKOWRON A. Rudiments of rough sets [J]. Information Sciences, 2007, 177(1): 3-27.
WANG Guoyin, YU Hong, YANG Dachun. Decision table reduction based on conditional information entropy [J]. Chinese Journal of Computers, 2002, 25(7): 759-766.
TING K. An instance-weighting method to induce cost-sensitive trees [J]. IEEE Transactions on Knowledge and Data Engineering, 2002, 14(3): 659-665.
XIE Hong, CHENG Haozhong, NIU Dongxiao. Discretization of continuous attributes in rough set theory based on information entropy [J]. Chinese Journal of Computers, 2005, 28(9): 1570-1574.
HU Qinghua, Xie Zongxia, YU Daren. Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation [J]. Pattern Recognition, 2007, 40(12): 3509-3521.
DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets [J]. International Journal of General Systems, 1990, 17(2): 191-209.
HU Qinghua, YU Daren, XIE Zongxia. Numerical attribute reduction based on neighborhood granulation and rough approximation [J]. Chinese Journal of Software, 2008, 19(3): 640-649.
HU Qinghua, LIU Jinfu, YU Daren. Mixed feature selection based on granulation and approximation [J]. Knowledge-Based Systems, 2008, 21(4): 294-304.
XU Changzhi, MIN Fan. Weighted reduction for decision tables [C]∥Proceedings of 3rd International Conference on Fuzzy Systems and Knowledge Discovery. Berlin, Germany: Springer-Verlag, 2006: 246-255.
HU Qinghua, YU Daren, XIE Zongxia, et al. Fuzzy probabilistic approximation spaces and their information measures [J]. IEEE Transactions on Fuzzy Systems, 2006, 14(2): 191-201.
LIU Jinfu, HU Qinghua, YU Daren. A weighted rough set based method developed for class imbalance learning [J]. Information Sciences, 2008, 178(4): 1235-1256.
LIU Yang, FENG Boqin, BAI Guohua. Compact rule learner on weighted fuzzy approximation spaces for class imbalanced and hybrid data [C]∥Proceedings of 6th International Conference on Rough Sets and Current Trends in Computing. Berlin, Gemany: Springer-Verlag, 2008: 262-271.
ZADEH L. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
LEE H. An optimal algorithm for computing the max-min transitive closure of a fuzzy similarity matrix [J]. Fuzzy Sets and Systems, 2001, 123(1): 129-136.
FRANK A, ASUNCION A. UCI machine learning repository [DB/OL]. [2010-12-22]. http:∥archive.ics.uci.edu/ml.
BREFELD U, GEIBEL P, WYSOTZKI F. Support vector machines with example dependent costs [C]∥Proceedings of the European Conference on Machine Learning. Berlin, Germany, Springer-Verlag, 2003:23-34.