# Attraction-Repulsion Spectrum in Neighbor Embeddings

arXiv: https://arxiv.org/abs/2007.08902 · HTML: https://mlsanity.com/paper/2007.08902/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2020.

## Built on by (most cited first, 30 of 41)

- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Unsupervised visualization of image datasets using contrastive learning](https://mlsanity.com/paper/2210.09879/) (2022)
- [Class-constrained t-SNE: Combining Data Features and Class Probabilities](https://mlsanity.com/paper/2308.13837/) (2023)
- [A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction](https://mlsanity.com/paper/2305.19043/) (2023)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [ParaDime: A Framework for Parametric Dimensionality Reduction](https://mlsanity.com/paper/2210.04582/) (2022)
- [Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold](https://mlsanity.com/paper/2401.17675/) (2024)
- [Large data limits and scaling laws for tSNE](https://mlsanity.com/paper/2410.13063/) (2024)
- [DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction](https://mlsanity.com/paper/2508.13747/) (2025)
- [Interpretable Dimensionality Reduction by Feature Preserving Manifold Approximation and Projection](https://mlsanity.com/paper/2211.09321/) (2022)
- [Relating tSNE and UMAP to Classical Dimensionality Reduction](https://mlsanity.com/paper/2306.11898/) (2023)
- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [Accelerating hyperbolic t-SNE](https://mlsanity.com/paper/2401.13708/) (2024)
- [Curvature Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2403.14813/) (2024)
- [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)
- [Collection Space Navigator: An Interactive Visualization Interface for Multidimensional Datasets](https://mlsanity.com/paper/2305.06809/) (2023)
- [Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation](https://mlsanity.com/paper/2406.09876/) (2024)
- [EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings](https://mlsanity.com/paper/2509.03703/) (2025)
- [Efficient and Robust Bayesian Selection of Hyperparameters in Dimension Reduction for Visualization](https://mlsanity.com/paper/2306.00357/) (2023)
- [Navigating Perplexity: A linear relationship with the data set size in t-SNE embeddings](https://mlsanity.com/paper/2308.15513/) (2023)
- [Graph Vertex Embeddings: Distance, Regularization and Community Detection](https://mlsanity.com/paper/2404.10784/) (2024)
- [FedNE: Surrogate-Assisted Federated Neighbor Embedding for Dimensionality Reduction](https://mlsanity.com/paper/2409.11509/) (2024)
- [Attraction-Repulsion Swarming: A Generalized Framework of t-SNE via Force Normalization and Tunable Interactions](https://mlsanity.com/paper/2411.10617/) (2024)
- [Dimensionality reduction for homological stability and global structure preservation](https://mlsanity.com/paper/2503.03156/) (2025)
- [Node Embeddings via Neighbor Embeddings](https://mlsanity.com/paper/2503.23822/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [FloDR: An invertible dimensionality reduction method based on a normalising flow](https://mlsanity.com/paper/2607.26278/) (2026)
- [On the Selection of Tuning Parameters for Patch-Stitching Embedding Methods](https://mlsanity.com/paper/2207.07218/) (2022)

## Abstract (arXiv)

Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using kNN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with a repulsive force between all points. One of the most popular examples of such algorithms is t-SNE. Here we empirically show that changing the balance between the attractive and the repulsive forces in t-SNE using the exaggeration parameter yields a spectrum of embeddings, which is characterized by a simple trade-off: stronger attraction can better represent continuous manifold structures, while stronger repulsion can better represent discrete cluster structures and yields higher kNN recall. We find that UMAP embeddings correspond to t-SNE with increased attraction; mathematical analysis shows that this is because the negative sampling optimisation strategy employed by UMAP strongly lowers the effective repulsion. Likewise, ForceAtlas2, commonly used for visualizing developmental single-cell transcriptomic data, yields embeddings corresponding to t-SNE with the attraction increased even more. At the extreme of this spectrum lie Laplacian Eigenmaps. Our results demonstrate that many prominent neighbor embedding algorithms can be placed onto the attraction-repulsion spectrum, and highlight the inherent trade-offs between them.