# Measuring the Data

arXiv: https://arxiv.org/abs/2504.02083 · HTML: https://mlsanity.com/paper/2504.02083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 2 Apr 2025.

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

- [The Sparse Manifold Transform](https://mlsanity.com/paper/1806.08887/) (2018)
- [Enhancing Neural Training via a Correlated Dynamics Model](https://mlsanity.com/paper/2312.13247/) (2023)
- [Improving Autoencoder Image Interpolation via Dynamic Optimal Transport](https://mlsanity.com/paper/2404.08900/) (2024)
- [Data representation with optimal transport](https://mlsanity.com/paper/2406.15503/) (2024)

## Abstract (arXiv)

Measuring the Data analytically finds the intrinsic manifold in big data. First, Optimal Transport generates the tangent space at each data point from which the intrinsic dimension is revealed. Then, the Koopman Dimensionality Reduction procedure derives a nonlinear transformation from the data to the intrinsic manifold. Measuring the data procedure is presented here, backed up with encouraging results.