基于超图对偶的二元表$D$ -基的发现
Discovery of the $D$-basis in binary tables based on hypergraph dualization
摘要：
发现（强）关联规则或隐含关系是数据管理中的一项重要任务，它在人工智能、数据采掘和语义Web中有着广泛的应用。我们介绍了一种新的方法，发现一组特定的影响，称为$D$的基础上，提供了一个表示为减少二进制表，基于其伽罗瓦格的结构。该方法的核心是格理论框架中定义的$D$ -关系，以及超图对偶算法，该算法使我们能够有效地产生给定Sperner超图的横截集。后一种算法首先由罗格斯运筹学中心的专家开发，已经在解决数据库理论、人工智能和博弈论中的优化问题中找到了许多应用。该方法的一个应用是分析与特定表型变量相关的基因表达数据，并对夏威夷大学癌症中心提供的数据进行了一些初步测试。
英文摘要：
Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a specific set of implications, called the $D$-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice. At the core of the method are the $D$-relation defined in the lattice theory framework, and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given Sperner hypergraph. The latter algorithm, first developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, artificial intelligence and game theory. One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the University of Hawaii Cancer Center.
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