IEEE VIS 2024 Content: GhostUMAP: Measuring Pointwise Instability in Dimensionality Reduction

GhostUMAP: Measuring Pointwise Instability in Dimensionality Reduction

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Myeongwon Jung - Sungkyunkwan University, Suwon, Korea, Republic of

 Takanori Fujiwara - Linköping University, Norrköping, Sweden

 Jaemin Jo - Sungkyunkwan University, Suwon, Korea, Republic of

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 Room: Bayshore VI

2024-10-16T13:24:00ZGMT-0600Change your timezone on the schedule page
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Exemplar figure, described by caption below — Each projection is part of a GhostUMAP projection generated for the CIFAR-10 dataset. Case (A) depicts the trajectories of a stable point where the original projection (blue cross) and its ghosts (blue triangles) are projected to a consistent location. In contrast, Case (B) shows the trajectories of an unstable point. The trajectories diverge, implying instability in the final projection of the point (orange cross).

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Keywords

Dimensionality Reduction

Abstract

Although many dimensionality reduction (DR) techniques employ stochastic methods for computational efficiency, such as negative sampling or stochastic gradient descent, their impact on the projection has been underexplored. In this work, we investigate how such stochasticity affects the stability of projections and present a novel DR technique, GhostUMAP, to measure the pointwise instability of projections. Our idea is to introduce clones of data points, “ghosts”, into UMAP’s layout optimization process. Ghosts are designed to be completely passive: they do not affect any others but are influenced by attractive and repulsive forces from the original data points. After a single optimization run, GhostUMAP can capture the projection instability of data points by measuring the variance with the projected positions of their ghosts. We also present a successive halving technique to reduce the computation of GhostUMAP. Our results suggest that GhostUMAP can reveal unstable data points with a reasonable computational overhead.