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

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• High-dimensional (HD) data analysis is challenged by dimensionality reduction (DR) techniques that often fail to preserve all original data structures.
• Existing DR methods focus on either local or global structures, potentially leading to misinterpretations of data manifolds.
• Local DR techniques may overemphasize manifold compactness, while global techniques can obscure well-separated clusters.

Purpose of the Study:

• To introduce Uniform Manifold Approximation with Two-phase Optimization (UMATO), a novel DR technique designed to capture both local and global data structures effectively.
• To address the limitations of existing DR methods in accurately representing complex HD data.
• To enhance the reliability of visual analytics for HD data.

Main Methods:

• UMATO employs a two-phase optimization process for dimensionality reduction.
• Phase one constructs a skeletal layout using representative points.
• Phase two projects remaining data points while preserving regional characteristics.

Main Results:

• UMATO demonstrates superior global structure preservation compared to UMAP and other widely used DR techniques.
• UMATO shows a slight, acceptable trade-off in local structure preservation.
• The technique exhibits enhanced scalability and stability against initialization and subsampling variations.

Conclusions:

• UMATO offers a more reliable approach to high-dimensional data analysis by balancing local and global structure preservation.
• The method's improved scalability and stability make it suitable for large and complex datasets.
• UMATO enhances the faithfulness of projections, thereby improving the reliability of visual analytics.