On the Lattice of Conceptual Measurements
This work provides a theoretical framework for understanding and manipulating data set scaling for researchers working with formal concept analysis.
This paper introduces a new method for data set scaling using scale-measures from formal concept analysis, which are continuous maps between closure systems. It demonstrates that these scale-measures are lattice ordered and can be explored using meet and join operations, and proves an isomorphism between the lattice of scale-measures and the lattice of sub-closure systems.
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.