# Local intrinsic dimensionality estimators based on concentration of measure

arXiv: https://arxiv.org/abs/2001.11739 · HTML: https://mlsanity.com/paper/2001.11739/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 5 of 5)

- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Intrinsic Dimension for Large-Scale Geometric Learning](https://mlsanity.com/paper/2210.05301/) (2022)
- [Impact of dataset size and long-term ECoG-based BCI usage on deep learning decoders performance](https://mlsanity.com/paper/2209.03789/) (2022)
- [Local Intrinsic Dimensional Entropy](https://mlsanity.com/paper/2304.02223/) (2023)
- [Dimensionality of datasets in object detection networks](https://mlsanity.com/paper/2210.07049/) (2022)

## Abstract (arXiv)

Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data point distribution, or computed locally in different regions of the data space. In this paper, we introduce new local estimators of ID based on linear separability of multi-dimensional data point clouds, which is one of the manifestations of concentration of measure. We empirically study the properties of these estimators and compare them with other recently introduced ID estimators exploiting various effects of measure concentration. Observed differences between estimators can be used to anticipate their behaviour in practical applications.