# Relating tSNE and UMAP to Classical Dimensionality Reduction

arXiv: https://arxiv.org/abs/2306.11898 · HTML: https://mlsanity.com/paper/2306.11898/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 81 references that are in the map.
- First posted on arXiv 20 Jun 2023.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [MedCLIP: Contrastive Learning from Unpaired Medical Images and Text](https://mlsanity.com/paper/2210.10163/) (2022)
- [Unified Contrastive Learning in Image-Text-Label Space](https://mlsanity.com/paper/2204.03610/) (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)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [Cold-start Active Learning through Self-supervised Language Modeling](https://mlsanity.com/paper/2010.09535/) (2020)
- [Supporting Clustering with Contrastive Learning](https://mlsanity.com/paper/2103.12953/) (2021)
- [Contrastive Learning of Musical Representations](https://mlsanity.com/paper/2103.09410/) (2021)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [A Broad Study on the Transferability of Visual Representations with Contrastive Learning](https://mlsanity.com/paper/2103.13517/) (2021)
- [Attract, Perturb, and Explore: Learning a Feature Alignment Network for Semi-supervised Domain Adaptation](https://mlsanity.com/paper/2007.09375/) (2020)
- [CoLA: Weakly-Supervised Temporal Action Localization with Snippet Contrastive Learning](https://mlsanity.com/paper/2103.16392/) (2021)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Your Classifier can Secretly Suffice Multi-Source Domain Adaptation](https://mlsanity.com/paper/2103.11169/) (2021)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [When Explainability Meets Adversarial Learning: Detecting Adversarial Examples using SHAP Signatures](https://mlsanity.com/paper/1909.03418/) (2019)
- [Unsupervised Domain Adaptation via Regularized Conditional Alignment](https://mlsanity.com/paper/1905.10885/) (2019)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [Feature Alignment and Restoration for Domain Generalization and Adaptation](https://mlsanity.com/paper/2006.12009/) (2020)
- [Domain Generalization via Optimal Transport with Metric Similarity Learning](https://mlsanity.com/paper/2007.10573/) (2020)
- [Minimum-Distortion Embedding](https://mlsanity.com/paper/2103.02559/) (2021)
- [Half a Percent of Labels is Enough: Efficient Animal Detection in UAV Imagery using Deep CNNs and Active Learning](https://mlsanity.com/paper/1907.07319/) (2019)
- [Sublinear Time Low-Rank Approximation of Positive Semidefinite Matrices](https://mlsanity.com/paper/1704.03371/) (2017)
- [Locally Linear Embedding and its Variants: Tutorial and Survey](https://mlsanity.com/paper/2011.10925/) (2020)
- [Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders](https://mlsanity.com/paper/2103.16046/) (2021)
- [Unsupervised and Supervised Principal Component Analysis: Tutorial](https://mlsanity.com/paper/1906.03148/) (2019)
- [Reducing the Covariate Shift by Mirror Samples in Cross Domain Alignment](https://mlsanity.com/paper/2110.06448/) (2021)

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

- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [Curvature Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2403.14813/) (2024)
- [Leveraging Convolutional and Graph Networks for an Unsupervised Remote Sensing Labelling Tool](https://mlsanity.com/paper/2508.00506/) (2025)

## Abstract (arXiv)

It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find semantic patterns in high-dimensional data without supervision. Despite this, gradient-based DR methods lack the most important quality that an explainability method should possess: themselves being explainable. That is, given a UMAP output, it is currently unclear what one can say about the corresponding input. We work towards closing this question by relating UMAP to classical DR techniques. Specifically, we show that one can fully recover methods like PCA, MDS, and ISOMAP in the modern DR paradigm: by applying attractions and repulsions onto a randomly initialized dataset. We also show that, with a small change, Locally Linear Embeddings (LLE) can indistinguishably reproduce UMAP outputs. This implies that the UMAP effective objective is minimized by this modified version of LLE (and vice versa). Given this, we discuss what must be true of UMAP emebddings and present avenues for future work.