%0 Journal Article %1 HANIKA2022453 %A Hanika, Tom %A Hirth, Johannes %D 2022 %J Information Sciences %K %P 453-468 %R https://doi.org/10.1016/j.ins.2022.09.005 %T On the lattice of conceptual measurements %U https://www.sciencedirect.com/science/article/pii/S0020025522010489 %V 613 %X 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.

@article{HANIKA2022453, 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.}, added-at = {2022-09-28T00:14:19.000+0200}, author = {Hanika, Tom and Hirth, Johannes}, biburl = {https://www.bibsonomy.org/bibtex/2752bc4553487e6472b22faf56e744cad/tomhanika}, doi = {https://doi.org/10.1016/j.ins.2022.09.005}, interhash = {ecd4e48ac83c8aea9197f7e3d861b032}, intrahash = {752bc4553487e6472b22faf56e744cad}, issn = {0020-0255}, journal = {Information Sciences}, keywords = {}, pages = {453-468}, timestamp = {2022-09-28T00:14:19.000+0200}, title = {On the lattice of conceptual measurements}, url = {https://www.sciencedirect.com/science/article/pii/S0020025522010489}, volume = 613, year = 2022 }