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Cluster structures and collections of Galois closed entity subsets

机译:伽罗瓦封闭实体子集的集群结构和集合

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We discuss relations between cluster structures and so-called cluster prestructures. On the other hand, we place ourselves in the framework of a context where entity descriptions belong to a complete meet-semilattice. Such a context induces a Galois correspondence which, in turn, induces a closure operator on the powerset of the entity set. We give a necessary and sufficient condition for a particular collection of fixed points of this closure operator to be hierarchical. Moreover, we specify the collection of all entity subsets which are both fixed points of this closure operator and strong clusters associated with a given pairwise dissimilarity function, as well as that of all entity subsets which are both fixed points of this closure operator and weak clusters associated with a given k-way dissimilarity function. (c) 2007 Elsevier B.V. All rights reserved.
机译:我们讨论了簇结构和所谓的簇预结构之间的关系。另一方面,我们将自己置于上下文描述的框架中,在该上下文中,实体描述属于完整的会面语义。这样的上下文产生了伽罗瓦对应关系,而后者又在实体集的幂集上引起了闭包运算符。我们为该闭包运算符的不动点的特定集合提供了必要的充分条件。此外,我们指定所有实体子集的集合,这些实体子集都是该闭合运算符的固定点和与给定成对的相异函数相关联的强簇,以及所有实体子集的集合,它们都是此闭合运算符和弱簇的固定点与给定的K向差异函数相关联。 (c)2007 Elsevier B.V.保留所有权利。

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