# Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE

arXiv: https://arxiv.org/abs/2405.17412 · HTML: https://mlsanity.com/paper/2405.17412/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 7 of 7)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [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)
- [Representation Uncertainty in Self-Supervised Learning as Variational Inference](https://mlsanity.com/paper/2203.11437/) (2022)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [Dimensionality Reduction as Probabilistic Inference](https://mlsanity.com/paper/2304.07658/) (2023)

## 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)
- [Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements](https://mlsanity.com/paper/2507.21040/) (2025)
- [Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2512.03899/) (2025)

## Abstract (arXiv)

This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate of the data precision matrix) using a Wishart distribution, with a mean given by a non-linear covariance function evaluated on the latents. This interpretation offers deeper theoretical and semantic insights into such algorithms, and forging a connection to Gaussian process latent variable models by showing that well-known kernels can be used to describe covariances implied by graph Laplacians. We also introduce tools with which similar dimensionality reduction methods can be studied.