属性约简矩阵特征结构及分层约简快速算法

已有的属性约简算法往往只能提供一个可行解,并且不能保证是最小约简解.因此,详细分析属性约简特征并获得最小约简解具有重要意义.本文针对信息系统数据集提出属性约简矩阵,通过矩阵的结构特征分析得到属性的约简特征,因此采用矩阵代数的方法求解属性约简问题,并得到分层约简快速算法.经实例运算可见,矩阵代数的处理和算法大大降低了最小约简解获取的计算量.

Structural features of attribute reduction matrix and layer fast algorithm

Current algorithms provide only feasible attribute reductions,they are not necessarily the minimum ones. Thus,it is significant to analyze the characteristics of attribute reduction and get the minimum one from all reductions. Firstly,an attribute reduction matrix is defined based on the information system.The attribute reduction can be characterized by the structural features of the matrix.Then,a layer fast algorithm by matrix algebraic theory is proposed to solve the problem.Finally,numerical results are given to show the advantage of our method by highly reducing the computational cost.