# On the Lattice of Conceptual Measurements

arXiv: https://arxiv.org/abs/2012.05267 · HTML: https://mlsanity.com/paper/2012.05267/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2020.

## Built on by (most cited first, 8 of 8)

- [Quantifying the Conceptual Error in Dimensionality Reduction](https://mlsanity.com/paper/2106.06815/) (2021)
- [Conceptual Views on Tree Ensemble Classifiers](https://mlsanity.com/paper/2302.05270/) (2023)
- [Exploring Scale-Measures of Data Sets](https://mlsanity.com/paper/2102.02576/) (2021)
- [Scaling Dimension](https://mlsanity.com/paper/2302.09101/) (2023)
- [Ordinal Motifs in Lattices](https://mlsanity.com/paper/2304.04827/) (2023)
- [Automatic Textual Explanations of Concept Lattices](https://mlsanity.com/paper/2304.08093/) (2023)
- [Conceptual Views of Neural Networks: A Framework for Neuro-Symbolic Analysis](https://mlsanity.com/paper/2209.13517/) (2022)
- [The Geometric Structure of Topic Models](https://mlsanity.com/paper/2403.03607/) (2024)

## Abstract (arXiv)

We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice ordered with respect to the closure systems. This enables exploring the set of scale-measures through by the use of meet and join operations. Furthermore we show that the lattice of scale-measures is isomorphic to the lattice of sub-closure systems that arises from the original data. Finally, we provide another representation of scale-measures using propositional logic in terms of data set features. Our theoretical findings are discussed by means of examples.