aiqbench analysis
This research introduces a graph-based method to mitigate "partial neighborhood embedding" in dimensionality reduction by splitting ambiguous data points into multiple projections. By replicating instances that belong to dissimilar neighborhoods, the technique preserves fine-grained local structures often lost in standard UMAP visualizations. This advancement offers researchers more accurate tools for analyzing high-dimensional datasets where traditional single-point mappings obscure complex relationships.
When One Point Is Not Enough: Addressing Ambiguous Instances in Dimensionality Reduction by Splitting
arXiv:2605.23540v2 Announce Type: replace Abstract: Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However, DR is an inherently lossy process; no technique can perfectly preserve the high-dimensional relationships, and projections therefore contain visual artifacts. In this paper, we highlight a typically overlooked source of visual artifacts: ambiguous instances. These are instances that are highly similar to multiple mutually dissimilar neighborhoods in the high-dimensional space. Standard DR methods cannot faithfully project such instances, since each data instance is mapped to a single point in the visual space. As a result, such an instance is placed in only one of its neighborhoods (or in none at all), so only part of its neighborhood structure is represented. We call this distortion partial neighborhood embedding. In this paper, we introduce a graph-based approach that identifies ambiguous instances and replicates them as multiple points in the projection, placing each copy within its respective neighborhood. We use UMAP for our results, but our approach also generalizes to other local graph-based DR techniques. We show that our approach reveals previously hidden neighborhood memberships in projections and reduces partial neighborhood embedding across multiple examples, and is further supported by quantitative analyses.
Abstract:Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However, DR is an inherently lossy process; no technique can perfectly preserve the high-dimensional relationships, and projections therefore contain visual artifacts. In this paper, we highlight a typically overlooked source of visual artifacts: ambiguous instances. These are instances that are highly similar to multiple mutually dissimilar neighborhoods in the high-dimensional space. Standard DR methods cannot faithfully project such instances, since each data instance is mapped to a single point in the visual space. As a result, such an instance is placed in only one of its neighborhoods (or in none at all), so only part of its neighborhood structure is represented. We call this distortion partial neighborhood embedding. In this paper, we introduce a graph-based approach that identifies ambiguous instances and replicates them as multiple points in the projection, placing each copy within its respective neighborhood. We use UMAP for our results, but our approach also generalizes to other local graph-based DR techniques. We show that our approach reveals previously hidden neighborhood memberships in projections and reduces partial neighborhood embedding across multiple examples, and is further supported by quantitative analyses.
Machine Learning (cs.LG)
arXiv:2605.23540 [cs.LG]
(or arXiv:2605.23540v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.23540 Focus to learn more arXiv-issued DOI via DataCite
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