Dependence space of matroids and its application to attribute reduction

TL;DR

This paper introduces a dependence space of matroids to enhance the understanding and optimization of attribute reduction in data mining, combining algebraic structures with rough set theory.

Contribution

It constructs a dependence space for matroids and characterizes key concepts like reducts, offering new methods for attribute reduction.

Findings

Characterization of consistent sets and reducts via matroids

Two expressions for matroid bases derived from the dependence space

New approaches to attribute reduction using algebraic structures

Abstract

Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy algorithm design, which plays an important role in attribute reduction. Therefore, it is meaningful to combine matroids with rough sets to solve the optimization problems. In this paper, we introduce an existing algebraic structure called dependence space to study the reduction problem in terms of matroids. First, a dependence space of matroids is constructed. Second, the characterizations for the space such as consistent sets and reducts are studied through matroids. Finally, we investigate matroids by the means of the space and present two expressions for their bases. In a word, this paper provides new approaches to study attribute reduction.