Towards Scaling‐Invariant Projections for Data Visualization

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...

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Vydané v:Computer graphics forum Ročník 44; číslo 2
Hlavní autori: Dierkes, Joel, Stelter, Daniel, Rössl, Christian, Theisel, Holger
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.05.2025
Predmet:
CCS Concepts
Human‐centered computing → Visualization techniques
Invariants
Multidimensional data
Optimization
Scaling
Scientific visualization
Visualization
Visualization systems and tools
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.70063