# From t-SNE to UMAP with contrastive learning

arXiv: https://arxiv.org/abs/2206.01816 · HTML: https://mlsanity.com/paper/2206.01816/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (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)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Keystroke Dynamics as Part of Lifelogging](https://mlsanity.com/paper/2010.10144/) (2020)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [Exploring the Limits of Language Modeling](https://mlsanity.com/paper/1602.02410/) (2016)
- [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)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [word2vec Explained: deriving Mikolov et al.'s negative-sampling word-embedding method](https://mlsanity.com/paper/1402.3722/) (2014)
- [Noise Contrastive Estimation and Negative Sampling for Conditional Models: Consistency and Statistical Efficiency](https://mlsanity.com/paper/1809.01812/) (2018)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (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)
- [Investigating the Role of Negatives in Contrastive Representation Learning](https://mlsanity.com/paper/2106.09943/) (2021)
- [Understanding Negative Samples in Instance Discriminative Self-supervised Representation Learning](https://mlsanity.com/paper/2102.06866/) (2021)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)

## Built on by (most cited first, 28 of 28)

- [Improving neural network representations using human similarity judgments](https://mlsanity.com/paper/2306.04507/) (2023)
- [Unsupervised visualization of image datasets using contrastive learning](https://mlsanity.com/paper/2210.09879/) (2022)
- [Dimension Reduction with Locally Adjusted Graphs](https://mlsanity.com/paper/2412.15426/) (2024)
- [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)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction](https://mlsanity.com/paper/2508.13747/) (2025)
- [Curvature Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2403.14813/) (2024)
- [Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE](https://mlsanity.com/paper/2405.17412/) (2024)
- [Navigating the Effect of Parametrization for Dimensionality Reduction](https://mlsanity.com/paper/2411.15894/) (2024)
- [Manifold Approximation leads to Robust Kernel Alignment](https://mlsanity.com/paper/2510.22953/) (2025)
- [Navigating Perplexity: A linear relationship with the data set size in t-SNE embeddings](https://mlsanity.com/paper/2308.15513/) (2023)
- [FedNE: Surrogate-Assisted Federated Neighbor Embedding for Dimensionality Reduction](https://mlsanity.com/paper/2409.11509/) (2024)
- [Generalizable Spectral Embedding with an Application to UMAP](https://mlsanity.com/paper/2501.11305/) (2025)
- [Node Embeddings via Neighbor Embeddings](https://mlsanity.com/paper/2503.23822/) (2025)
- [CLEAR: Unlearning Spurious Style-Content Associations with Contrastive LEarning with Anti-contrastive Regularization](https://mlsanity.com/paper/2507.18794/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [Supervised Stochastic Neighbor Embedding Using Contrastive Learning](https://mlsanity.com/paper/2309.08077/) (2023)
- [AKRMap: Adaptive Kernel Regression for Trustworthy Visualization of Cross-Modal Embeddings](https://mlsanity.com/paper/2505.14664/) (2025)
- [Feature Space Analysis by Guided Diffusion Model](https://mlsanity.com/paper/2509.07936/) (2025)
- [Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2512.03899/) (2025)
- [IPBC: An Interactive Projection-Based Framework for Human-in-the-Loop Semi-Supervised Clustering of High-Dimensional Data](https://mlsanity.com/paper/2601.18828/) (2026)
- [mlx-vis: GPU-Native Dimensionality Reduction on Apple Silicon](https://mlsanity.com/paper/2603.04035/) (2026)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [On Out-of-sample Embedding in UMAP](https://mlsanity.com/paper/2606.04451/) (2026)
- [CosMAP: Contrastive Manifold Approximation and Projection for Dimensionality Reduction of Omics and Genealogical Data](https://mlsanity.com/paper/2608.11269/) (2026)
- [Say, Echo, Do: Strategic Narratives and Revealed Positioning in Financial Markets](https://mlsanity.com/paper/2609.38545/) (2026)
- [ibUMAP: Coherent and Scalable Field Evaluation for UMAP Optimization](https://mlsanity.com/paper/2610.01445/) (2026)

## Abstract (arXiv)

Neighbor embedding methods t-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly differing embeddings and can suggest conflicting interpretations of the same data. The fundamental reasons for this and, more generally, the exact relationship between t-SNE and UMAP have remained unclear. In this work, we uncover their conceptual connection via a new insight into contrastive learning methods. Noise-contrastive estimation can be used to optimize t-SNE, while UMAP relies on negative sampling, another contrastive method. We find the precise relationship between these two contrastive methods and provide a mathematical characterization of the distortion introduced by negative sampling. Visually, this distortion results in UMAP generating more compact embeddings with tighter clusters compared to t-SNE. We exploit this new conceptual connection to propose and implement a generalization of negative sampling, allowing us to interpolate between (and even extrapolate beyond) t-SNE and UMAP and their respective embeddings. Moving along this spectrum of embeddings leads to a trade-off between discrete / local and continuous / global structures, mitigating the risk of over-interpreting ostensible features of any single embedding. We provide a PyTorch implementation.