# Scaling Dimension

arXiv: https://arxiv.org/abs/2302.09101 · HTML: https://mlsanity.com/paper/2302.09101/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 17 Feb 2023.

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

- [On the Lattice of Conceptual Measurements](https://mlsanity.com/paper/2012.05267/) (2020)
- [Intrinsic Dimension of Geometric Data Sets](https://mlsanity.com/paper/1801.07985/) (2018)
- [Quantifying the Conceptual Error in Dimensionality Reduction](https://mlsanity.com/paper/2106.06815/) (2021)
- [What is the dimension of your binary data?](https://mlsanity.com/paper/1902.01480/) (2019)
- [Conceptual Views on Tree Ensemble Classifiers](https://mlsanity.com/paper/2302.05270/) (2023)
- [Conceptual Views of Neural Networks: A Framework for Neuro-Symbolic Analysis](https://mlsanity.com/paper/2209.13517/) (2022)

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

- [Automatic Textual Explanations of Concept Lattices](https://mlsanity.com/paper/2304.08093/) (2023)
- [Conceptual Mapping of Controversies](https://mlsanity.com/paper/2404.18940/) (2024)

## Abstract (arXiv)

Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic definitions are in flux. Our contribution was triggered by the study of concept lattices for tree classifiers and the scaling methods used there. We extend some basic notions, give precise mathematical definitions for them and introduce the concept of scaling dimension. In addition to a detailed discussion of its properties, including an example, we show theoretical bounds related to the order dimension of concept lattices. We also study special subclasses, such as the ordinal and the interordinal scaling dimensions, and show for them first results and examples.