基于矩阵列秩属性优先的概念格算法

An Algorithm of Concept Lattice Based on Matrix Column Rank with Attribute Priority

基于矩阵列秩的理论以及概念对并运算封闭的特征,提出了一种基于矩阵列秩属性优先的概念格的生成算法.首先,将形式概念分析中数据的形式背景看成一个0-1矩阵,利用矩阵的秩定义出概念的秩.其次,通过概念的秩的定义和概念对并运算封闭的特征,对概念按秩进行分层提取.通过对形式概念分析中数据的形式背景与矩阵的某些性质之间的联系的探索以及实例的验证,表明该算法行之有效.

Based on the theory of the matrix column rank and the characterization that the concept is closed for join, this paper presents an algorithm of concept lattice based on matrix column rank with attribute priority. Firstly, we consider the data represented by the formal context in the formal conceptual anal- ysis as a 0-1 matrix, and simultaneously, the rank of some concepts is defined by the rank of matrix. Secondly, using the definition of the rank of concepts and the characterization that the concept is closed for join, we derive concept for the layer according to the rank. After the study on the relation between the data represented by the formal context and some properties of matrices, and besides on a real example indicate that, the algorithm presented above, is effective.