When One Point Is Not Enough: Addressing Ambiguous Instances in Dimensionality Reduction by Splitting
Authors
Diede P M van der Hoorn (Eindhoven University of Technology), Alessio Arleo (Eindhoven University of Technology), Fernando V Paulovich (TU Eindhoven)
Presentation
- Session
- That's way too many dimensions for me
- Time
- Thursday, Nov 12, 10:00 – 10:12 (US/Eastern) · session 10:00 – 11:30
- Location
- Hall Essex north
Links
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Keywords
Dimensionality Reduction, Ambiguity, Partial Neighborhood Embedding
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.
For Practitioners
This paper is relevant to data scientist, machine learning engineers, visualization researchers, bioinformaticians and other analysts who use dimensionality reduction techniques such as UMAP and t-SNE to explore high-dimensional data. The work is particularly useful in domains where local neighborhood structure is important for interpretation. We show that standard dimensionality reduction methods can obscure data instances that belong to multiple distinct neighborhoods, potentially leading to incomplete or misleading interpretations. Practitioners can use the proposed approach to identify such ambiguous instances and explicitly visualize their multiple neighborhood memberships.