Coarsest granularity-based optimal reduct using A^* search

Abstract

The optimal reduct computation problem aims to obtain the best reduct out of all possible reducts of a given decision system. In the rough set literature, two optimality criteria exist for computing an optimal reduct: shortest length based and coarsest granular space based. The coarsest granular space-based optimal reduct has the ability to induce a better generalizable classification model. The $A^*RSOR$ is an existing $A^*$ search-based optimal reduct computation algorithm that uses the coarsest granular space as an optimality criterion. This article proposes an improved coarsest granularity-based optimal reduct approach $MA^*\_RSOR$ through analyzing the search process’s behaviour in $A^*RSOR$ algorithm. To minimize the search space utilization and arrive at an optimal reduct in less time, suitable modifications are incorporated using the domain knowledge of rough set theory. The relevance of $MA^*\_RSOR$ is demonstrated through theoretical analysis and comparative experimental validation with state-of-the-art algorithms. The experimental results with benchmark data sets established that $MA^*\_RSOR$ achieves significant computational time gain ($49-99\%$) and space reduction ($37-96\%$) over $A^*RSOR$. The $MA^*\_RSOR$ could induce classification models with significantly better classification accuracies than state-of-the-art shortest length-based optimal/near-optimal reduct computation algorithms. In addition, a coefficient of variation based $CV_{\text {NonCore}}$ heuristic is proposed for predicting when the $MA^*\_RSOR$ algorithm is appropriate to use. Experimental results validate the relevance of the heuristic as its prediction turned out correctly in 8 out of 10 data sets.