# UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction

arXiv: https://arxiv.org/abs/2508.16227 · HTML: https://mlsanity.com/paper/2508.16227/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 95 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 29 of 29)

- [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)
- [Automated Hate Speech Detection and the Problem of Offensive Language](https://mlsanity.com/paper/1703.04009/) (2017)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [UIBert: Learning Generic Multimodal Representations for UI Understanding](https://mlsanity.com/paper/2107.13731/) (2021)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [ActiVis: Visual Exploration of Industry-Scale Deep Neural Network Models](https://mlsanity.com/paper/1704.01942/) (2017)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiples](https://mlsanity.com/paper/1912.04853/) (2019)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [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)
- [ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings](https://mlsanity.com/paper/2308.00282/) (2023)
- [Automatic Selection of t-SNE Perplexity](https://mlsanity.com/paper/1708.03229/) (2017)
- [Uniform Manifold Approximation with Two-phase Optimization](https://mlsanity.com/paper/2205.00420/) (2022)
- [Representation Selective Self-distillation and wav2vec 2.0 Feature Exploration for Spoof-aware Speaker Verification](https://mlsanity.com/paper/2204.02639/) (2022)
- [Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2308.00278/) (2023)
- [VitaLITy: Promoting Serendipitous Discovery of Academic Literature with Transformers & Visual Analytics](https://mlsanity.com/paper/2108.03366/) (2021)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [Large-Scale Evaluation of Topic Models and Dimensionality Reduction Methods for 2D Text Spatialization](https://mlsanity.com/paper/2307.11770/) (2023)
- [A Critical Analysis of the Usage of Dimensionality Reduction in Four Domains](https://mlsanity.com/paper/2503.08836/) (2025)
- ["Normalized Stress" is Not Normalized: How to Interpret Stress Correctly](https://mlsanity.com/paper/2408.07724/) (2024)
- [GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP](https://mlsanity.com/paper/2507.17174/) (2025)
- [Understanding Bias in Perceiving Dimensionality Reduction Projections](https://mlsanity.com/paper/2507.20805/) (2025)

## Built on by (most cited first, 1 of 1)

- [Class Angular Distortion Index for Dimensionality Reduction](https://mlsanity.com/paper/2605.00637/) (2026)

## Abstract (arXiv)

Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local neighborhood structures (local techniques) or global structures such as pairwise distances between points (global techniques). However, both approaches can mislead analysts to erroneous conclusions about the overall arrangement of manifolds in HD data. For example, local techniques may exaggerate the compactness of individual manifolds, while global techniques may fail to separate clusters that are well-separated in the original space. In this research, we provide a deeper insight into Uniform Manifold Approximation with Two-phase Optimization (UMATO), a DR technique that addresses this problem by effectively capturing local and global structures. UMATO achieves this by dividing the optimization process of UMAP into two phases. In the first phase, it constructs a skeletal layout using representative points, and in the second phase, it projects the remaining points while preserving the regional characteristics. Quantitative experiments validate that UMATO outperforms widely used DR techniques, including UMAP, in terms of global structure preservation, with a slight loss in local structure. We also confirm that UMATO outperforms baseline techniques in terms of scalability and stability against initialization and subsampling, making it more effective for reliable HD data analysis. Finally, we present a case study and a qualitative demonstration that highlight UMATO's effectiveness in generating faithful projections, enhancing the overall reliability of visual analytics using DR.