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.

翻译：给定一个形式背景，序因子是其关联关系的一个子集，在概念格中构成一条链，即对应于线性顺序的数据集部分。为了可视化形式背景中的数据，Ganter和Glodeanu提出了一种基于两个序因子的双标图。为使该双标图有效，这些因子需包含尽可能多的数据点，即覆盖关联关系的大部分。本文研究了这类序二元因子分解。首先，我们探讨了在省略序二元因子分解的形式背景中两个因子的不相交性。然后，我们证明判定给定规模的二元因子分解是否存在是一个NP完全问题，这使得计算最大因子分解在计算上代价高昂。最后，我们提出了Ord2Factor算法，可用于计算大规模的序二元因子分解。