Attribute Reduction in Decision-Theoretic Rough Set Model using Particle Swarm Optimization with the Threshold Parameters Determined using LMS Training Rule

Decision-theoretic rough set model is the probabilistic generalization of the Pawlak rough set model. In this paper, we have analyzed decision-theoretic rough set model (DTRSM) in the context of attribute reduction. DTRSM is based on Bayesian decision theory for classifying an object into a particular category. The risk associated with classifying an object is defined in terms of loss functions and conditional probabilities. We have used least mean squares learning algorithm to determine the Bayesian loss functions by taking expected overall risk as the learning function. With the loss functions ready, DTRSM can be applied to classification problems. We have proposed attribute reduction in DTRSM by optimizing the expected overall risk using particle swarm optimization algorithm. The proposed algorithm was tested on various data sets found in University of California, machine learning repository. The proposed algorithm has given good results for the cardinality of the reduct and classification accuracy during tests performed on the data sets. Experimental results obtained by the proposed algorithm have been found to give better reduced length of the reduct and classification accuracy in comparison to the results obtained by the consistency subset evaluation feature selection algorithm described in the literature.