# On Out-of-sample Embedding in UMAP

arXiv: https://arxiv.org/abs/2606.04451 · HTML: https://mlsanity.com/paper/2606.04451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 60 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [MedCLIP: Contrastive Learning from Unpaired Medical Images and Text](https://mlsanity.com/paper/2210.10163/) (2022)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Mapping the stereotyped behaviour of freely-moving fruit flies](https://mlsanity.com/paper/1310.4249/) (2013)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [Manifold-aligned Neighbor Embedding](https://mlsanity.com/paper/2205.11257/) (2022)
- [ActUp: Analyzing and Consolidating tSNE and UMAP](https://mlsanity.com/paper/2305.07320/) (2023)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [Self Organizing Nebulous Growths for Robust and Incremental Data Visualization](https://mlsanity.com/paper/1912.04896/) (2019)
- [Outlier Detection in Large Radiological Datasets using UMAP](https://mlsanity.com/paper/2407.21263/) (2024)
- [Navigating the Effect of Parametrization for Dimensionality Reduction](https://mlsanity.com/paper/2411.15894/) (2024)
- [Deep Recursive Embedding for High-Dimensional Data](https://mlsanity.com/paper/2104.05171/) (2021)
- [Coverage Hole Detection for mmWave Networks: An Unsupervised Learning Approach](https://mlsanity.com/paper/2108.07854/) (2021)
- [Visualization of Emergency Department Clinical Data for Interpretable Patient Phenotyping](https://mlsanity.com/paper/1907.11039/) (2019)
- [Manifold Learning for Personalized and Label-Free Detection of Cardiac Arrhythmias](https://mlsanity.com/paper/2506.16494/) (2025)

## Abstract (arXiv)

Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space. An increasingly popular algorithm is Uniform Manifold Learning and Projection (UMAP), which uses algebraic topology to map distances between the two spaces. While it works well on many types of data sets, UMAP has trouble adding out-of-sample points to a pre-existing mapping. In particular, UMAP often places new points on the periphery of the found clusters, rather than in their interiors with their correlated neighbors. Here, we overcome this ``repulsion effect'' by optimizing pairwise interactions within the original k-nearest-neighbor graph. Moreover, we show that parameterizing UMAP obtains better embeddings than non-parametric algorithms, particularly as the data gets more complex (e.g., medical images). We also show that the repulsion effect is naturally mitigated when a parameterized UMAP is employed to embed the data. We characterize different UMAP approaches using trustworthiness, nearest neighbor classifiers, and by analyzing attractive and repulsive forces in the embeddings.