Towards Scaling-Invariant Projections for Data Visualization
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Finding projections of multidimensional data domains to the 2D screen space is a well-known problem. Multidimensional data often comes with the property that the dimensions are measured in different physical units, which renders the ratio between dimensions, i.e., their scale, arbitrary. The result of common projections, like PCA, t-SNE, or MDS, depends on this ratio, i.e., these projections are variant to scaling. This results in an undesired subjective view of the data, and thus, their projection. Simple solutions like normalization of each dimension are widely used, but do not always give high-quality results. We propose to visually analyze the space of all scalings and to find optimal scalings w.r.t. the quality of the visualization. For this, we evaluate different quality criteria on scatter plots. Given a quality criterion, our approach finds scalings that yield good visualizations with little to no user input using numerical optimization. Simultaneously, our method results in a scaling invariant projection, proposing an objective view to the projected data. We show for several examples that such an optimal scaling can significantly improve the visualization quality.
Description
CCS Concepts: Human-centered computing → Visualization techniques; Visualization systems and tools
@article{10.1111:cgf.70063,
journal = {Computer Graphics Forum},
title = {{Towards Scaling-Invariant Projections for Data Visualization}},
author = {Dierkes, Joel and Stelter, Daniel and Rössl, Christian and Theisel, Holger},
year = {2025},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70063}
}