mlsanityData to 14 Oct 2026

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

arXiv 2508.16227 ↗First posted 22 Aug 2025cs.LGcited by 1

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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.

Key facts. Cited by 1 paper 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

29 of 95 references.

References · 29

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  6. 2020Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualizationcited by 173
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17 more
  1. 2019Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiplescited by 38
  2. 2021Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Studycited by 27
  3. 2019Supporting Analysis of Dimensionality Reduction Results with Contrastive Learningcited by 26
  4. 2021Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projectionscited by 20
  5. 2020Bringing UMAP Closer to the Speed of Light with GPU Accelerationcited by 19
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  8. 2022Uniform Manifold Approximation with Two-phase Optimizationcited by 12
  9. 2022Representation Selective Self-distillation and wav2vec 2.0 Feature Exploration for Spoof-aware Speaker Verificationcited by 11
  10. 2023Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reductioncited by 11
  11. 2021VitaLITy: Promoting Serendipitous Discovery of Academic Literature with Transformers & Visual Analyticscited by 10
  12. 2022Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patternscited by 8
  13. 2023Large-Scale Evaluation of Topic Models and Dimensionality Reduction Methods for 2D Text Spatializationcited by 8
  14. 2025A Critical Analysis of the Usage of Dimensionality Reduction in Four Domainscited by 7
  15. 2024"Normalized Stress" is Not Normalized: How to Interpret Stress Correctlycited by 5
  16. 2025GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAPcited by 1
  17. 2025Understanding Bias in Perceiving Dimensionality Reduction Projectionscited by 1

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Citing papers per year: 2026: 1.

1 paper.

  1. 2026Class Angular Distortion Index for Dimensionality Reductioncited by 0