论文标题
在概念测量的格子上
On the Lattice of Conceptual Measurements
论文作者
论文摘要
我们基于正式概念分析（即闭合系统之间的连续图）的规模测量提出了一种新的数据集缩放方法，并得出了规范表示。此外，我们证明说规模测量是相对于闭合系统的晶格订购的。这使通过使用和加入操作通过使用和加入操作来探索一组规模测量。此外，我们表明，比例测量的晶格与原始数据产生的亚封闭系统的晶格是同构的。最后，我们在数据集特征方面使用命题逻辑提供了比例尺测量的另一种表示。我们的理论发现是通过示例讨论的。
We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice ordered with respect to the closure systems. This enables exploring the set of scale-measures through by the use of meet and join operations. Furthermore we show that the lattice of scale-measures is isomorphic to the lattice of sub-closure systems that arises from the original data. Finally, we provide another representation of scale-measures using propositional logic in terms of data set features. Our theoretical findings are discussed by means of examples.
