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

2025-08-22

AI Summary

Dimensionality reduction of high-dimensional data often struggles to simultaneously preserve local structure (e.g., UMAP) and global structure (e.g., t-SNE, PCA): local methods may distort the overall manifold topology, while global ones can erroneously merge well-separated clusters. To address this, we propose UMATO—a two-stage optimization method built upon the UMAP framework. In the first stage, representative points are selected to construct a “skeleton layout” that preserves global topological relationships; in the second stage, remaining points are projected onto this skeleton according to regional geometric characteristics. This design explicitly harmonizes local neighborhood fidelity with global manifold alignment consistency. Experiments demonstrate that UMATO outperforms state-of-the-art methods—including UMAP—across key metrics: global structural preservation, scalability, initialization robustness, and subsampling stability. Consequently, UMATO significantly enhances the reliability and interpretability of visual analytics.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Search and Optimization: Local Search
• Data Mining & Knowledge Management: Data Visualization & Summarization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Bridging local and global structure preservation in dimensionality reduction
• Addressing misleading visual representations in high-dimensional data analysis
• Improving reliability of manifold arrangement visualization through optimized projection

Innovation

• Two-phase optimization process for dimensionality reduction
• Skeletal layout construction with representative points
• Preserves both local and global structural characteristics