Myeongwon Jung | Search arXiv

arXiv2026

GPUMAP: GPU-Accelerated Progressive Uniform Manifold Approximation and Projection

Dimensionality reduction (DR) techniques are fundamental to the analysis of high-dimensional data, yet their substantial computational cost limits their use in interactive settings. To address this limitation, we present GPU-accelerated Progressive Uniform Manifold Approximation and Projection (GPUMAP), an efficient progressive DR algorithm designed for interactive use. We identify three atomic operations within UMAP and restructure them into a progressive pipeline. As part of this adaptation, we introduce modifications to UMAP, including operation queues, instance-wise local join, and scheduling strategies. We further accelerate computation by leveraging GPU parallelism, enabling interactive analysis of million-scale datasets on commodity GPU hardware. Finally, we employ our implementation to systematically study the behavior of progressive DR, investigating how projections evolve over time relative to the ground-truth projection and how biased data streams influence the quality and stability of the resulting projections.

cs.LG↗

arXiv2025

GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP

Despite the widespread use of Uniform Manifold Approximation and Projection (UMAP), the impact of its stochastic optimization process on the results remains underexplored. We observed that it often produces unstable results where the projections of data points are determined mostly by chance rather than reflecting neighboring structures. To address this limitation, we introduce (r,d)-stability to UMAP: a framework that analyzes the stochastic positioning of data points in the projection space. To assess how stochastic elements, specifically initial projection positions and negative sampling, impact UMAP results, we introduce "ghosts", or duplicates of data points representing potential positional variations due to stochasticity. We define a data point's projection as (r,d)-stable if its ghosts perturbed within a circle of radius r in the initial projection remain confined within a circle of radius d for their final positions. To efficiently compute the ghost projections, we develop an adaptive dropping scheme that reduces a runtime up to 60% compared to an unoptimized baseline while maintaining approximately 90% of unstable points. We also present a visualization tool that supports the interactive exploration of the (r,d)-stability of data points. Finally, we demonstrate the effectiveness of our framework by examining the stability of projections of real-world datasets and present usage guidelines for the effective use of our framework.

cs.GR↗