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, for which we derive a canonical representation. Moreover, we prove that scale-measures can be lattice ordered using the canonical representation. This enables exploring the set of scale-measures 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.

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