Sample Pair Selection for Attribute Reduction with Rough Set

Abstract

Attribute reduction is the strongest and most characteristic result in rough set theory to distinguish itself to other theories. In the framework of rough set, an approach of discernibility matrix and function is the theoretical foundation of finding reducts. In this paper, sample pair selection with rough set is proposed in order to compress the discernibility function of a decision table so that only minimal elements in the discernibility matrix are employed to find reducts. First relative discernibility relation of condition attribute is defined, indispensable and dispensable condition attributes are characterized by their relative discernibility relations and key sample pair set is defined for every condition attribute. With the key sample pair sets, all the sample pair selections can be found. Algorithms of computing one sample pair selection and finding reducts are also developed; comparisons with other methods of finding reducts are performed with several experiments which imply sample pair selection is effective as preprocessing step to find reducts.

Attribute reduction: a horizontal data decomposition approach

“…Reducts are computed based on the discernibility function in disjunctive normal form. Chen et al (2012) proposed sample pair selection to construct the simplest form of the discernibility function of a decision table. Thanks to that, only minimal elements of the discernibility matrix are used to compute reducts.…”

Exploring the Boundary Region for Attribute Reduction in Inconsistent Decision Tables

“…As we all know, many researchers [3,16,22,23,24] employed discernibility matrix for attribute reduction. For small datasets, we can generate discernibility matrix to compute all reducts or a reduct.…”

“…Ngugen [12] and Korzeń [6] implemented efficient heuristic algorithms for acquiring a reduct through computing discernibility object pairs. Chen et al [3] proposed an attribute reduction method using sample pair selection for all reducts. In order to further accelerate attribute reduction for large inconsistent decision tables without constructing discernibility matrix, we must design a more reasonable uncertainty measure to evaluate discernibility information.…”

Attribute Reduction Based on Consistent Covering Rough Set and Its Application

“…Attribute reduction has become an important step in pattern recognition and machine learning tasks [1,2]. The main goal of attribute reduction is to remove redundant information in datasets and draw useful information so as to improve classification ability [3].…”

“…Supervised discretization methods generally include discretization based on information entropy and discretization based on ChiMerge algorithm [10], while unsupervised discretization methods arguably include box method for equal frequency or equal width, intuitive division discretization, and discretization based on cluster analysis [11,12]. There are two limitations in traditional attribute reduction based on rough set theory: (1) databases are numerical in the real world, so that they cannot be handled directly by traditional rough set theory; (2) numerical data have to be discretized before attribute reduction, which inevitably leads to information loss. Therefore, it is desirable to develop an efficient method which can deal with numerical databases directly.…”