# Learning Locally Adaptive Metrics that Enhance Structural Representation with textttLAMINAR

arXiv: https://arxiv.org/abs/2411.08557 · HTML: https://mlsanity.com/paper/2411.08557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 3 of 3)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms](https://mlsanity.com/paper/2307.05750/) (2023)
- [Learning Distances from Data with Normalizing Flows and Score Matching](https://mlsanity.com/paper/2407.09297/) (2024)

## Abstract (arXiv)

We present textttLAMINAR, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often rely on standard metrics to define geometric relationships in data, which may fail to capture the underlying structure of complex data sets. textttLAMINAR addresses this by using a continuous-normalising-flow and inverse-transform-sampling to define a Riemannian manifold in the data space without the need for the user to specify a metric over the data a-priori. The result is a locally-adaptive-metric that produces structurally-informative density-based distances. We demonstrate the utility of textttLAMINAR by comparing its output to the Euclidean metric for structured data sets.