%0 Generic %1 durrschnabel2023maximal %A Dürrschnabel, Dominik %A Stumme, Gerd %D 2023 %K 2023 itegpub myown np_complete ordinal_factor_analysis two_dimension_extension %T Maximal Ordinal Two-Factorizations %U http://arxiv.org/abs/2304.03338 %X Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.

@misc{durrschnabel2023maximal, abstract = {Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.}, added-at = {2023-12-13T15:18:36.000+0100}, author = {Dürrschnabel, Dominik and Stumme, Gerd}, biburl = {https://www.bibsonomy.org/bibtex/29dcf7585ac17738cf869999490083a41/stumme}, interhash = {c9681a551e3d5b8ef0591dcd6017baf1}, intrahash = {9dcf7585ac17738cf869999490083a41}, keywords = {2023 itegpub myown np_complete ordinal_factor_analysis two_dimension_extension}, note = {cite arxiv:2304.03338Comment: 14 pages, 6 figures, 2 algorithms}, timestamp = {2023-12-13T15:22:44.000+0100}, title = {Maximal Ordinal Two-Factorizations}, url = {http://arxiv.org/abs/2304.03338}, year = 2023 }