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CLUSTER ANALYSIS BASED ON TANGLES IN ABSTRACT SEPARATIONS SYSTEMS
CLUSTER ANALYSIS BASED ON TANGLES IN ABSTRACT SEPARATIONS SYSTEMS
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机译：抽象分离系统中基于纠缠的聚类分析
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摘要
A computer-implemented method to capture and detect clusters in, or determined by, a set V of discrete digital data comprising; • computing, from the set V, an abstract separation system ASS that consists of a finite set S, whose elements are called separations; of a predetermined transitive, antisymmetric and reflexive order relation ≤ on S; and of an order-reversing involution * : S→ S, that is, a mapping s → s* with the property that, (s*)* = s and that r ≤ s implies s* r* for all r, s ∈ S; • predetermining a set of consistency requirements (CRs), that is, a set F of subsets of S;• computing, from the ASS (S, ≤, ∗), one or more abstract tangles, that is, any set T ⊆ S that contains exactly one of each pair {s, s* } for s ∈ S, and does not contain any of the forbidden configurations F ∈ F as a subset; or determining that there is no abstract tangle; and • determining that any abstract tangle T represents a cluster in, or determined by, the data set V.展开▼
机译：一种计算机实现的方法，用于捕获和检测一组离散数字数据中的簇或由其确定的簇。 •从集合 V 中计算一个抽象分离系统 ASS，该ASS由有限集合 S 组成，其元素称为分离。 S 上预定的传递，反对称和反身顺序关系≤和逆序对合*： S → S ，即映射 s → s *具有（ s *）* = s 且r≤ s 的性质表示 s * 对于所有 r ， s ∈ S 的I> r *; •预先确定一组一致性要求（CR），即 S 的子集的一组 F ;•从ASS（ S ，≤，∗），一个或多个抽象缠结，即，任何一组T⊆S恰好包含每对{ s ， s *}表示 s ∈ S ，并且不包含任何禁止配置 F ∈< I> F 作为子集;或确定没有抽象纠缠; •确定任何抽象缠结 T 表示数据集 V中的簇或由其确定。
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