属性拓扑与属性偏序双向转化
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摘要
属性拓扑和属性偏序是近年来新提出的两种形式背景表示方法。其中,属性拓扑基于属性耦合关系实现形式背景的简洁可视化表示,并发展出多种形式概念计算方法。属性偏序则以偏序关系为基础表示形式背景。针对两种新方法在形式概念分析领域中的互补关系,本文从集合论的角度论述属性拓扑与属性偏序双向转化的数学基础,描述不同二元关系下二者的转化原理与方法,并在此基础上提出属性拓扑和属性偏序双向转化算法,实现二者等价可逆转化,为形式背景提供统一的表示基础。
Attribute topology and attribute partial order are put forw ard to represent formal context recently. Based on the coupling betw een attributes,the simple visual representation of the formal context is achieved by attribute topology and the various forms of calculation methods are developed. Additionally,attribute partial order is based on partial order to represent formal concept. For the complementary relationships betw een the tw o new methods in the field of formal concept analysis,the mathematical basis of the bidirectional transformation of attribute topology and attribute partial order are discussed from the perspective of set theory on this paper,w here the transformation principles and methods of them are described in different binary relations. And the algorithm of the bidirectional transformation of attribute topology and attribute partial order based on the above is put forw ard,equivalent reversible conversion of them is achieved,and an unified representation basis for formal context is provided.
Attribute topology and attribute partial order are put forw ard to represent formal context recently. Based on the coupling betw een attributes,the simple visual representation of the formal context is achieved by attribute topology and the various forms of calculation methods are developed. Additionally,attribute partial order is based on partial order to represent formal concept. For the complementary relationships betw een the tw o new methods in the field of formal concept analysis,the mathematical basis of the bidirectional transformation of attribute topology and attribute partial order are discussed from the perspective of set theory on this paper,w here the transformation principles and methods of them are described in different binary relations. And the algorithm of the bidirectional transformation of attribute topology and attribute partial order based on the above is put forw ard,equivalent reversible conversion of them is achieved,and an unified representation basis for formal context is provided.
引文
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[2]kopljanac-Mac(ina F,Bla2kovic'B.Formal concept analysis overview and applications[J].Procedia Engineering,2014,69:1258-1267.
[3]JIANG Ping,REN Sheng-bing,LIN Juan.Using formal concept analysis for software engineering[J].Computer Technology and Development,2008,18(4):127-129.
[4]MEHDI Kaytoue,SERGEI O Kuznetsov,AMEDEO Napoli,et al.Mining gene expression data with pattern structures in formal concept analysis[J].Information Sciences,2011,181(10):1989-2001.
[5]HELEN Gibson,SIMONAndrews,KONSTANTINOS Domdouzi,etal.Combining big social media data and FCA for crisis response[C]//IEEE/ACM 7th International Conference on Utility and Cloud Computing,2014:690-695.
[6]汤亚强,范敏,李金海.三元形式概念分析下的认知系统模型及信息粒转化方法[J].山东大学学报,2014,49(8):102-106.
[7]ANDREA Spoto,LUCA Stefanutti,GIULIO Vidotto.Knowledge space theory,formal concept analysis,and computerized psychological assessment[J].Behavior Research Methods,2010,42(1):342-350.
[8]JAOUA A,ELLOUMI S.Galois connection,formal concepts and Galois lattice in real relations:application in a real classifier[J].Journal of Systems&Software,2002,60(1):149-163.
[9]张涛,洪文学,路静.形式背景的属性树表示[J].系统工程理论与实践,2011,31(2):197-202.
[10]ZHANG Yanyan,WANG Xiaomin,WANG Jinkuan,et al.A visualization method of huge video/image databases based on formal concept analysis and the attribute partial order theory[C]//International Congress on Image&Signal Processing.IEEE,2013:165-169.
[11]张涛,任宏雷.形式背景的属性拓扑表示[J].小型微型计算机系统,2014,35(3):590-593.
[12]张涛,任宏雷,洪文学,等.基于属性拓扑的可视化形式概念计算[J].电子学报,2014,42(5):925-932.
[13]李刚,马彦超,张涛,等.基于属性拓扑图的形式概念构造算法[J].系统工程理论与实践,2015,35(1):254-259.
[14]ZHANG Tao,LI Hui,HONG Wenxue,et al.Deep First Formal Concept Search[J].The Scientific World Journal,2014(8):275679.
[15]洪文学,李少雄,张涛,等.大数据偏序结构生成原理[J].燕山大学学报,2014,38(5):388-393,402
[16]LIU Xulong,HONG Wenxue,SONG Jialin,et al.Using formal concept analysis to visualize relationships of syndromes in traditional Chinese medicine[C]//International Conference on Medical Biometrics,Hong Kong,2010:315-324.
[17]HONG Wenxue,LUAN Jingmin,LIU Xulong,et al.Inquiring diagnosis system of traditional Chinese medicine[C]//International Conference on Instrumentation,Measurement,Computer,Communication and Control,IEEE,2011:92-96.
[18]靖鲲鹏,宋之杰.基于属性偏序结构图的文本型灾情信息可视化[J].灾害学,2014,29(3):27-63.
[19]FAN Fengjie,HONG Wenxue,LI Xin,et al.Research on Compatibility of Prescription of TCP Based on the Principle of Attribute Partial Order Chart[C]//International Conference on Instrumentation,Measurement,Computer,Communication&Control,IEEE,2011:82-86.
[20]ZHANG W,WEI L,QI J.Attribute reduction theory and approach to concept lattice[J].Science in China Series F:Information Sciences,2005,48(6):713-726.