# Quantifying the Conceptual Error in Dimensionality Reduction

arXiv: https://arxiv.org/abs/2106.06815 · HTML: https://mlsanity.com/paper/2106.06815/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 12 Jun 2021.

## Builds on (most cited first, 2 of 2)

- [NIMFA: A Python Library for Nonnegative Matrix Factorization](https://mlsanity.com/paper/1808.01743/) (2018)
- [On the Lattice of Conceptual Measurements](https://mlsanity.com/paper/2012.05267/) (2020)

## Built on by (most cited first, 6 of 6)

- [Scaling Dimension](https://mlsanity.com/paper/2302.09101/) (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)
- [Towards Ordinal Data Science](https://mlsanity.com/paper/2307.09477/) (2023)
- [The Geometric Structure of Topic Models](https://mlsanity.com/paper/2403.03607/) (2024)
- [Conceptual Mapping of Controversies](https://mlsanity.com/paper/2404.18940/) (2024)

## Abstract (arXiv)

Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore, a wide variety of reduction procedures are in use, each pursuing different objectives. A so far not considered criterion is the conceptual continuity of the reduction mapping, i.e., the preservation of the conceptual structure with respect to the original data set. Based on the notion scale-measure from formal concept analysis we present in this work a) the theoretical foundations to detect and quantify conceptual errors in data scalings; b) an experimental investigation of our approach on eleven data sets that were respectively treated with a variant of non-negative matrix factorization.