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On the Lattice of Conceptual Measurements

T. Hanika, and J. Hirth. (2020)cite arxiv:2012.05267Comment: 19 pages, 6 figures.

Abstract

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.

Description

On the Lattice of Conceptual Measurements

Links and resources

URL:
https://arxiv.org/abs/2012.05267
BibTeX key:
hanika2020lattice
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