Solving the Attribute Reduction Problem with Ant Colony Optimization

Attribute reduction is an important process in rough set theory. More minimal attribute reductions are expected to help clients make decisions in some cases, though the minimal attribute reduction problem (MARP) is proved to be a NP-hard problem. In this paper, we propose a new heuristic approach for solving the MARP based on the ant colony optimization (ACO) metaheuristic. We first model the MARP as finding an assignment which minimizes the cost in a graph. Afterward, we introduce a preprocessing step that removes the redundant data in a discernibility matrix through the absorbtion operator, the goal of which is to favor a smaller exploration of the search space at a lower cost. We then develop a new algorithm R-ACO for solving the MARP. Finally, the simulation results show that our approach can find more minimal attribute reductions more efficiently in most cases.

[1]  XU Guang-hua,et al.  Reduction of rough set attribute based on immune clone selection , 2006 .

[2]  Wang Guo,et al.  Decision Table Reduction based on Conditional Information Entropy , 2002 .

[3]  Wang Guo.  Calculation Methods for Core Attributes of Decision Table , 2003 .

[4]  Yiyu Yao,et al.  Discernibility matrix simplification for constructing attribute reducts , 2009, Inf. Sci..

[5]  Dominik Slezak,et al.  Attribute Reduction in the Bayesian Version of Variable Precision Rough Set Model , 2003, RSKD.

[6]  Guoyin Wang,et al.  Rule generation based on rough set theory , 2000, SPIE Defense + Commercial Sensing.

[7]  Wang Jue,et al.  A reduction algorithm meeting users' requirements , 2002 .

[8]  Wei-Zhi Wu,et al.  Knowledge reduction in random information systems via Dempster-Shafer theory of evidence , 2005, Inf. Sci..

[9]  Jan G. Bazan,et al.  Rough set algorithms in classification problem , 2000 .

[10]  Christine Solnon,et al.  Ants can solve constraint satisfaction problems , 2002, IEEE Trans. Evol. Comput..

[11]  Wang Ju,et al.  Reduction algorithms based on discernibility matrix: The ordered attributes method , 2001, Journal of Computer Science and Technology.

[12]  Xin-xia Wang,et al.  An Improved Ant Colony Optimization Applied to Attributes Reduction , 2008, ACFIE.

[13]  Marco Dorigo,et al.  Ant colony optimization theory: A survey , 2005, Theor. Comput. Sci..

[14]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

[15]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[16]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[17]  Xiangyang Wang,et al.  Feature selection based on rough sets and particle swarm optimization , 2007, Pattern Recognit. Lett..

[18]  Zuren Feng,et al.  An efficient ant colony optimization approach to attribute reduction in rough set theory , 2008, Pattern Recognit. Lett..

[19]  Yezheng Liu,et al.  An Attribute Reduction Method Based on Ant Colony Optimization , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[20]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.

[21]  Wei-Zhi Wu,et al.  A general approach to attribute reduction in rough set theory , 2007, Science in China Series F: Information Sciences.