# Ordinal Motifs in Lattices

arXiv: https://arxiv.org/abs/2304.04827 · HTML: https://mlsanity.com/paper/2304.04827/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Builds on (most cited first, 6 of 6)

- [On interestingness measures of formal concepts](https://mlsanity.com/paper/1611.02646/) (2016)
- [On the Lattice of Conceptual Measurements](https://mlsanity.com/paper/2012.05267/) (2020)
- [Knowledge Cores in Large Formal Contexts](https://mlsanity.com/paper/2002.11776/) (2020)
- [Clones in Graphs](https://mlsanity.com/paper/1802.07849/) (2018)
- [Exploring Scale-Measures of Data Sets](https://mlsanity.com/paper/2102.02576/) (2021)
- [Force-Directed Layout of Order Diagrams using Dimensional Reduction](https://mlsanity.com/paper/2102.02684/) (2021)

## Built on by (most cited first, 2 of 2)

- [The Geometric Structure of Topic Models](https://mlsanity.com/paper/2403.03607/) (2024)
- [Conceptual Topic Aggregation](https://mlsanity.com/paper/2506.22309/) (2025)

## Abstract (arXiv)

Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set.