# Beyond kNN: Adaptive, Sparse Neighborhood Graphs via Optimal Transport

arXiv: https://arxiv.org/abs/2208.00604 · HTML: https://mlsanity.com/paper/2208.00604/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 1 Aug 2022.

## Builds on (most cited first, 8 of 8)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Regularized Optimal Transport and the Rot Mover's Distance](https://mlsanity.com/paper/1610.06447/) (2016)
- [Manifold learning with bi-stochastic kernels](https://mlsanity.com/paper/1711.06711/) (2017)
- [Dynamical Optimal Transport on Discrete Surfaces](https://mlsanity.com/paper/1809.07083/) (2018)
- [Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to Heteroskedastic Noise](https://mlsanity.com/paper/2006.00402/) (2020)
- [Quadratically regularized optimal transport](https://mlsanity.com/paper/1903.01112/) (2019)
- [An adaptive nearest neighbor rule for classification](https://mlsanity.com/paper/1905.12717/) (2019)

## Built on by (most cited first, 3 of 3)

- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)
- [Quadratically Regularized Optimal Transport: nearly optimal potentials and convergence of discrete Laplace operators](https://mlsanity.com/paper/2212.00103/) (2022)
- [Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis](https://mlsanity.com/paper/2605.24644/) (2026)

## Abstract (arXiv)

Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point. However, the kNN heuristic may become inappropriate when sampling density or noise level varies across datasets. Strategies that try to get around this typically introduce additional parameters that need to be tuned. We propose a simple approach to construct an adaptive neighbourhood graph from a single parameter, based on quadratically regularised optimal transport. Our numerical experiments show that graphs constructed in this manner perform favourably in unsupervised and semi-supervised learning applications.