%0 Conference Paper %1 10.1007/978-3-031-40960-8_5 %A Dürrschnabel, Dominik %A Stumme, Gerd %B Graph-Based Representation and Reasoning %C Cham %D 2023 %E Ojeda-Aciego, Manuel %E Sauerwald, Kai %E Jäschke, Robert %I Springer Nature Switzerland %K 2023 factorization myown ordinal_factor_analysis two_dimensional %P 41--55 %T Maximal Ordinal Two-Factorizations %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 \$\$\backslashtextsf\NP\\$\$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. %@ 978-3-031-40960-8

@inproceedings{10.1007/978-3-031-40960-8_5, 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 {\$}{\$}{\backslash}textsf{\{}NP{\}}{\$}{\$}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 = {2023-12-13T16:26:27.000+0100}, address = {Cham}, author = {Dürrschnabel, Dominik and Stumme, Gerd}, biburl = {https://www.bibsonomy.org/bibtex/2ab45693c5282706c6aa20a36c0b3e8dd/duerrschnabel}, booktitle = {Graph-Based Representation and Reasoning}, editor = {Ojeda-Aciego, Manuel and Sauerwald, Kai and Jäschke, Robert}, interhash = {c9681a551e3d5b8ef0591dcd6017baf1}, intrahash = {ab45693c5282706c6aa20a36c0b3e8dd}, isbn = {978-3-031-40960-8}, keywords = {2023 factorization myown ordinal_factor_analysis two_dimensional}, pages = {41--55}, publisher = {Springer Nature Switzerland}, timestamp = {2024-01-03T10:40:33.000+0100}, title = {Maximal Ordinal Two-Factorizations}, year = 2023 }