# Parametric UMAP embeddings for representation and semi-supervised learning

arXiv: https://arxiv.org/abs/2009.12981 · HTML: https://mlsanity.com/paper/2009.12981/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2020.

## Built on by (most cited first, 30 of 104)

- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [MatSciBERT: A Materials Domain Language Model for Text Mining and Information Extraction](https://mlsanity.com/paper/2109.15290/) (2021)
- [V2A-Mapper: A Lightweight Solution for Vision-to-Audio Generation by Connecting Foundation Models](https://mlsanity.com/paper/2308.09300/) (2023)
- [Reverse Engineering Self-Supervised Learning](https://mlsanity.com/paper/2305.15614/) (2023)
- [Learning Topology-Preserving Data Representations](https://mlsanity.com/paper/2302.00136/) (2023)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Geometric Autoencoders -- What You See is What You Decode](https://mlsanity.com/paper/2306.17638/) (2023)
- [WildVis: Open Source Visualizer for Million-Scale Chat Logs in the Wild](https://mlsanity.com/paper/2409.03753/) (2024)
- [DLME: Deep Local-flatness Manifold Embedding](https://mlsanity.com/paper/2207.03160/) (2022)
- [Unsupervised visualization of image datasets using contrastive learning](https://mlsanity.com/paper/2210.09879/) (2022)
- [Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction](https://mlsanity.com/paper/2203.12997/) (2022)
- [Bridging Vision and Language Spaces with Assignment Prediction](https://mlsanity.com/paper/2404.09632/) (2024)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset](https://mlsanity.com/paper/2203.04183/) (2022)
- [DiffAug: Enhance Unsupervised Contrastive Learning with Domain-Knowledge-Free Diffusion-based Data Augmentation](https://mlsanity.com/paper/2309.07909/) (2023)
- [GenURL: A General Framework for Unsupervised Representation Learning](https://mlsanity.com/paper/2110.14553/) (2021)
- [UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projection](https://mlsanity.com/paper/2207.03809/) (2022)
- [How people talk about each other: Modeling Generalized Intergroup Bias and Emotion](https://mlsanity.com/paper/2209.06687/) (2022)
- [ActUp: Analyzing and Consolidating tSNE and UMAP](https://mlsanity.com/paper/2305.07320/) (2023)
- [A General Approach for Determining Applicability Domain of Machine Learning Models](https://mlsanity.com/paper/2406.05143/) (2024)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [Exploring Adversarial Attacks and Defenses in Vision Transformers trained with DINO](https://mlsanity.com/paper/2206.06761/) (2022)
- [ParaDime: A Framework for Parametric Dimensionality Reduction](https://mlsanity.com/paper/2210.04582/) (2022)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [An embedding-based distance for temporal graphs](https://mlsanity.com/paper/2401.12843/) (2024)
- [Image-guided topic modeling for interpretable privacy classification](https://mlsanity.com/paper/2409.18674/) (2024)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections](https://mlsanity.com/paper/2504.16831/) (2025)
- [Dimension Reduction with Prior Information for Knowledge Discovery](https://mlsanity.com/paper/2111.13646/) (2021)

## Abstract (arXiv)

UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a graphical representation of a dataset (fuzzy simplicial complex), and (2) Through stochastic gradient descent, optimize a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that Parametric UMAP performs comparably to its non-parametric counterpart while conferring the benefit of a learned parametric mapping (e.g. fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semi-supervised learning by capturing structure in unlabeled data. Google Colab walkthrough: https://colab.research.google.com/drive/1WkXVZ5pnMrm17m0YgmtoNjM_XHdnE5Vp?usp=sharing