# Uniform Manifold Approximation with Two-phase Optimization

arXiv: https://arxiv.org/abs/2205.00420 · HTML: https://mlsanity.com/paper/2205.00420/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 1 May 2022.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Clustrophile 2: Guided Visual Clustering Analysis](https://mlsanity.com/paper/1804.03048/) (2018)
- [Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning](https://mlsanity.com/paper/1905.03911/) (2019)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [Bringing UMAP Closer to the Speed of Light with GPU Acceleration](https://mlsanity.com/paper/2008.00325/) (2020)

## Built on by (most cited first, 12 of 12)

- [CloChat: Understanding How People Customize, Interact, and Experience Personas in Large Language Models](https://mlsanity.com/paper/2402.15265/) (2024)
- [ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings](https://mlsanity.com/paper/2308.00282/) (2023)
- [Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2308.00278/) (2023)
- [CLAMS: A Cluster Ambiguity Measure for Estimating Perceptual Variability in Visual Clustering](https://mlsanity.com/paper/2308.00284/) (2023)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Metric Design != Metric Behavior: Improving Metric Selection for the Unbiased Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2507.02225/) (2025)
- [Dataset-Adaptive Dimensionality Reduction](https://mlsanity.com/paper/2507.11984/) (2025)
- [GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP](https://mlsanity.com/paper/2507.17174/) (2025)
- [UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2508.16227/) (2025)
- [pyBibX -- A Python Library for Bibliometric and Scientometric Analysis Powered with Artificial Intelligence Tools](https://mlsanity.com/paper/2304.14516/) (2023)
- [Detecting Suspicious Commenter Mob Behaviors on YouTube Using Graph2Vec](https://mlsanity.com/paper/2311.05791/) (2023)
- [Navigating High-Dimensional Backstage: A Guide for Exploring Literature for the Reliable Use of Dimensionality Reduction](https://mlsanity.com/paper/2506.14820/) (2025)

## Abstract (arXiv)

We introduce Uniform Manifold Approximation with Two-phase Optimization (UMATO), a dimensionality reduction (DR) technique that improves UMAP to capture the global structure of high-dimensional data more accurately. In UMATO, optimization is divided into two phases so that the resulting embeddings can depict the global structure reliably while preserving the local structure with sufficient accuracy. In the first phase, hub points are identified and projected to construct a skeletal layout for the global structure. In the second phase, the remaining points are added to the embedding preserving the regional characteristics of local areas. Through quantitative experiments, we found that UMATO (1) outperformed widely used DR techniques in preserving the global structure while (2) producing competitive accuracy in representing the local structure. We also verified that UMATO is preferable in terms of robustness over diverse initialization methods, number of epochs, and subsampling techniques.