# Maximal Ordinal Two-Factorizations

arXiv: https://arxiv.org/abs/2304.03338 · HTML: https://mlsanity.com/paper/2304.03338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 4 of 4)

- [Drawing Order Diagrams Through Two-Dimension Extension](https://mlsanity.com/paper/1906.06208/) (2019)
- [Attribute Selection using Contranominal Scales](https://mlsanity.com/paper/2106.10978/) (2021)
- [Greedy Discovery of Ordinal Factors](https://mlsanity.com/paper/2302.11554/) (2023)
- [Discovering Locally Maximal Bipartite Subgraphs](https://mlsanity.com/paper/2211.10446/) (2022)

## Built on by (most cited first, 1 of 1)

- [Towards Ordinal Data Science](https://mlsanity.com/paper/2307.09477/) (2023)

## Abstract (arXiv)

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.