# Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization

arXiv: https://arxiv.org/abs/2012.04456 · HTML: https://mlsanity.com/paper/2012.04456/

## Key facts

- Cited by 173 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 30 of 173)

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- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
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- [TabMT: Generating tabular data with masked transformers](https://mlsanity.com/paper/2312.06089/) (2023)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [Learning Topology-Preserving Data Representations](https://mlsanity.com/paper/2302.00136/) (2023)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Using Sequences of Life-events to Predict Human Lives](https://mlsanity.com/paper/2306.03009/) (2023)
- [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)
- [T-JEPA: Augmentation-Free Self-Supervised Learning for Tabular Data](https://mlsanity.com/paper/2410.05016/) (2024)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [DendroMap: Visual Exploration of Large-Scale Image Datasets for Machine Learning with Treemaps](https://mlsanity.com/paper/2205.06935/) (2022)
- [Improving Metric Dimensionality Reduction with Distributed Topology](https://mlsanity.com/paper/2106.07613/) (2021)
- [t-SNE, Forceful Colorings and Mean Field Limits](https://mlsanity.com/paper/2102.13009/) (2021)
- [Self-supervised visual learning from interactions with objects](https://mlsanity.com/paper/2407.06704/) (2024)
- [Towards an Explainable Comparison and Alignment of Feature Embeddings](https://mlsanity.com/paper/2506.06231/) (2025)
- [Dimension Reduction with Locally Adjusted Graphs](https://mlsanity.com/paper/2412.15426/) (2024)
- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [HLSFactory: A Framework Empowering High-Level Synthesis Datasets for Machine Learning and Beyond](https://mlsanity.com/paper/2405.00820/) (2024)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [DiffAug: Enhance Unsupervised Contrastive Learning with Domain-Knowledge-Free Diffusion-based Data Augmentation](https://mlsanity.com/paper/2309.07909/) (2023)
- [Integrating Chain-of-Thought and Retrieval Augmented Generation Enhances Rare Disease Diagnosis from Clinical Notes](https://mlsanity.com/paper/2503.12286/) (2025)
- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [A Spectral Method for Assessing and Combining Multiple Data Visualizations](https://mlsanity.com/paper/2210.13711/) (2022)

## Abstract (arXiv)

Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMAP have demonstrated impressive visualization performance on many real world datasets. One tension that has always faced these methods is the trade-off between preservation of global structure and preservation of local structure: these methods can either handle one or the other, but not both. In this work, our main goal is to understand what aspects of DR methods are important for preserving both local and global structure: it is difficult to design a better method without a true understanding of the choices we make in our algorithms and their empirical impact on the lower-dimensional embeddings they produce. Towards the goal of local structure preservation, we provide several useful design principles for DR loss functions based on our new understanding of the mechanisms behind successful DR methods. Towards the goal of global structure preservation, our analysis illuminates that the choice of which components to preserve is important. We leverage these insights to design a new algorithm for DR, called Pairwise Controlled Manifold Approximation Projection (PaCMAP), which preserves both local and global structure. Our work provides several unexpected insights into what design choices both to make and avoid when constructing DR algorithms.