# A Comparative Study of UMAP and Other Dimensionality Reduction Methods

arXiv: https://arxiv.org/abs/2603.02275 · HTML: https://mlsanity.com/paper/2603.02275/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 50 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [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)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Clustering with t-SNE, provably](https://mlsanity.com/paper/1706.02582/) (2017)

## Abstract (arXiv)

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including Principal Component Analysis (PCA), Kernel PCA, Sliced Inverse Regression (SIR), Kernel SIR, and t-distributed Stochastic Neighbor Embedding, through a comprehensive comparative analysis. Although UMAP has attracted substantial attention for preserving local and global structures, its supervised extensions, particularly for regression settings, remain rather underexplored. We provide a systematic evaluation of supervised UMAP for both regression and classification using simulated and real datasets, with performance assessed via predictive accuracy on low-dimensional embeddings. Our results show that supervised UMAP performs well for classification but exhibits limitations in effectively incorporating response information for regression, highlighting an important direction for future development.