Dependence space of matroids and its application to attribute reduction
This work addresses optimization problems in attribute reduction for data mining applications, but it appears incremental as it applies existing algebraic structures to a known bottleneck.
The paper tackles attribute reduction in knowledge representation and data mining by combining matroids with rough sets, constructing a dependence space of matroids to study reduction problems and characterize consistent sets and reducts.
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.