# Intrinsic dimension estimation for discrete metrics

arXiv: https://arxiv.org/abs/2207.09688 · HTML: https://mlsanity.com/paper/2207.09688/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 1 of 1)

- [DADApy: Distance-based Analysis of DAta-manifolds in Python](https://mlsanity.com/paper/2205.03373/) (2022)

## Built on by (most cited first, 4 of 4)

- [From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks](https://mlsanity.com/paper/2307.02279/) (2023)
- [Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification](https://mlsanity.com/paper/2405.15132/) (2024)
- [Unsupervised detection of semantic correlations in big data](https://mlsanity.com/paper/2411.02126/) (2024)
- [Density Estimation via Binless Multidimensional Integration](https://mlsanity.com/paper/2407.08094/) (2024)

## Abstract (arXiv)

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.