# What is the textitintrinsic dimension of your binary data? -- and how to compute it quickly

arXiv: https://arxiv.org/abs/2404.06326 · HTML: https://mlsanity.com/paper/2404.06326/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 9 Apr 2024.

## Builds on (most cited first, 7 of 7)

- [Intrinsic Dimension of Geometric Data Sets](https://mlsanity.com/paper/1801.07985/) (2018)
- [Relative intrinsic dimensionality is intrinsic to learning](https://mlsanity.com/paper/2311.07579/) (2023)
- [Intrinsic Dimension for Large-Scale Geometric Learning](https://mlsanity.com/paper/2210.05301/) (2022)
- [From-Below Approximations in Boolean Matrix Factorization: Geometry and New Algorithm](https://mlsanity.com/paper/1306.4905/) (2013)
- [What is the dimension of your binary data?](https://mlsanity.com/paper/1902.01480/) (2019)
- [Distances between Data Sets Based on Summary Statistics](https://mlsanity.com/paper/1902.01334/) (2019)
- [Formal concept analysis for evaluating intrinsic dimension of a natural language](https://mlsanity.com/paper/2311.10862/) (2023)

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

- [Unsupervised detection of semantic correlations in big data](https://mlsanity.com/paper/2411.02126/) (2024)

## Abstract (arXiv)

Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized correlation dimension. In the present work we revisit their results and contrast them with a concept based notion of intrinsic dimension (ID) recently introduced for geometric data sets. To do this, we present a novel approximation for this ID that is based on computing concepts only up to a certain support value. We demonstrate and evaluate our approximation using all available datasets from Tatti et al., which have between 469 and 41271 extrinsic dimensions.