# Towards Ordinal Data Science

arXiv: https://arxiv.org/abs/2307.09477 · HTML: https://mlsanity.com/paper/2307.09477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 224 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 24 of 24)

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Generalization Error Bound for Hyperbolic Ordinal Embedding](https://mlsanity.com/paper/2105.10475/) (2021)
- [Ordinal Non-negative Matrix Factorization for Recommendation](https://mlsanity.com/paper/2006.01034/) (2020)
- [Intrinsic Dimension of Geometric Data Sets](https://mlsanity.com/paper/1801.07985/) (2018)
- [Knowledge Cores in Large Formal Contexts](https://mlsanity.com/paper/2002.11776/) (2020)
- [What relations are reliably embeddable in Euclidean space?](https://mlsanity.com/paper/1903.05347/) (2019)
- [Quantifying the Conceptual Error in Dimensionality Reduction](https://mlsanity.com/paper/2106.06815/) (2021)
- [Relevant Attributes in Formal Contexts](https://mlsanity.com/paper/1812.08868/) (2018)
- [FCA2VEC: Embedding Techniques for Formal Concept Analysis](https://mlsanity.com/paper/1911.11496/) (2019)
- [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)
- [Intrinsic Dimension for Large-Scale Geometric Learning](https://mlsanity.com/paper/2210.05301/) (2022)
- [Formal Context Generation using Dirichlet Distributions](https://mlsanity.com/paper/1809.11160/) (2018)
- [Greedy Discovery of Ordinal Factors](https://mlsanity.com/paper/2302.11554/) (2023)
- [On the Usability of Probably Approximately Correct Implication Bases](https://mlsanity.com/paper/1701.00877/) (2017)
- [Clones in Graphs](https://mlsanity.com/paper/1802.07849/) (2018)
- [Probably approximately correct learning of Horn envelopes from queries](https://mlsanity.com/paper/1807.06149/) (2018)
- [Force-Directed Layout of Order Diagrams using Dimensional Reduction](https://mlsanity.com/paper/2102.02684/) (2021)
- [DimDraw -- A novel tool for drawing concept lattices](https://mlsanity.com/paper/1903.00686/) (2019)
- [Deep Ordinal Reinforcement Learning](https://mlsanity.com/paper/1905.02005/) (2019)
- [Orometric Methods in Bounded Metric Data](https://mlsanity.com/paper/1907.09239/) (2019)
- [The Mont Blanc of Twitter: Identifying Hierarchies of Outstanding Peaks in Social Networks](https://mlsanity.com/paper/2110.13774/) (2021)
- [Maximal Ordinal Two-Factorizations](https://mlsanity.com/paper/2304.03338/) (2023)

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

- [Conceptual Mapping of Controversies](https://mlsanity.com/paper/2404.18940/) (2024)

## Abstract (arXiv)

Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason -- particularly important for this line of research -- is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and 'calculating' with ordinal structures -- a specific class of directed graphs -- and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics.