# Exploring Scale-Measures of Data Sets

arXiv: https://arxiv.org/abs/2102.02576 · HTML: https://mlsanity.com/paper/2102.02576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [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)
- [Relevant Attributes in Formal Contexts](https://mlsanity.com/paper/1812.08868/) (2018)

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

- [Ordinal Motifs in Lattices](https://mlsanity.com/paper/2304.04827/) (2023)
- [The Geometric Structure of Topic Models](https://mlsanity.com/paper/2403.03607/) (2024)

## Abstract (arXiv)

Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of understandable and efficient scaling methods is at hand. A profound theory for scaling data is scale-measures, as developed in the field of formal concept analysis. Recent developments indicate that the set of all scale-measures for a given data set constitutes a lattice and does hence allow efficient exploring algorithms. In this work we study the properties of said lattice and propose a novel scale-measure exploration algorithm that is based on the well-known and proven attribute exploration approach. Our results motivate multiple applications in scale recommendation, most prominently (semi-)automatic scaling.