基于图属性拓扑的增量式等势概念计算  

Incremental equiconcept calculation based on graph attibute topology

作　　者：张涛[1] 薛在发 卢辉斌[1] 李少泽 张菁 刘学君[2] ZHANG Tao;XUE Zai-fa;LU Hui-bin;LI Shao-ze;ZHANG Jing;LIU Xue-jun(School of Information Science and Engineering,Yanshan University,Qinhuangdao 066004,China;School of Information Engineering and Academy of Artificial Intelligence,Beijing Institute of Petrochemical Technology,Beijing 102617,China)

机构地区：[1]燕山大学信息科学与工程学院,河北秦皇岛066004 [2]北京石油化工学院信息工程学院人工智能研究院,北京102617

出　　处：《控制与决策》2024年第10期3328-3336,共9页Control and Decision

基　　金：国家自然科学基金项目(62176229);河北省重点实验室项目(202250701010046);河北省在读研究生创新能力培养项目(CXZZBS2023046)。

摘　　要：等势概念是形式概念分析和概念认知学习的一个新兴课题,为社交网络分析提供了新的思路.现有的等势概念计算方法先搜索所有的形式概念再对其进行过滤,降低计算效率.随着增量式计算的发展,实现增量式等势概念的计算是一项重要的研究课题.为了解决上述问题,提出一种基于图属性拓扑的增量式等势概念计算方法.针对等势概念属性与对象的数量一致性特点,该方法通过对属性拓扑的结构进行优化,定义图形式背景下的图属性拓扑,进而证明图属性拓扑中极大完全多边形与等势概念一一对应的关系,并将此性质与属性拓扑的形式概念搜索算法相结合,提出静态图形式背景下直接计算等势概念的方法;基于此,进一步研究新增属性和新增对象对图属性拓扑中极大完全多边形的影响,完成增量式等势概念的直接计算.实验表明,直接计算方法能够有效提升等势概念的计算速度,并验证了所提出增量式等势概念更新计算的可行性和高效性.The equiconcept is a new topic in formal concept analysis and concept-cognitive learning,which provides a new idea for social network analysis.However,the existing equiconcept calculation methods first search out all formal concepts and then filter them,which reduces the calculation efficiency.And with the development of incremental computing,it is an important research topic to realize the calculation of the incremental equiconcept.To solve the above problems,this paper proposes an equiconcept calculation method based on incremental graph attribute topology.In view of the quantitative consistency between the attribute and object of the equiconcept,the proposed method defines the graph attribute topology on the graph formal context by optimizing the structure of the attribute topology.Furthermore,the one-to-one correspondence between the maximal complete polygon and the equiconcept in the graph property topology is proved.Combining this property with the formal concept search algorithm of the attribute topology,a method for directly calculating equiconcepts on the static graph formal context is proposed.On this basis,the influence of the new attribute and object on the maximal complete polygon in the graph attribute topology is further studied,and the direct calculation of incremental equiconcepts is completed.Experiments show that the direct calculation method can effectively improve the calculation speed of the equiconcept,and verify the feasibility and effectiveness of the proposed incremental equiconcept updating calculation.

关 键 词：形式概念分析 概念认知学习 等势概念 增量计算 属性拓扑 极大完全多边形 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]