Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields

Visualizing correlations, i.e., the tendency of uncertain data values at different spatial positions to change contrarily or according to each other, allows inferring on the possible variations of structures in the data. Visualizing global correlation structures, however, is extremely challenging, s...

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Vydáno v:Computer graphics forum Ročník 31; číslo 3pt2; s. 1025 - 1034
Hlavní autoři: Pfaffelmoser, Tobias, Westermann, Rüdiger
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford, UK Blackwell Publishing Ltd 01.06.2012
Témata:
Analysis
Clusters
Computer graphics
Correlation
I.3.3 [Computer Graphics]: Picture/Image Generation-Display algorithms
I.3.3 [Computer Graphics]: Picture/Image Generation—Display algorithms, Viewing algorithms
Random variables
Samples
Scalars
Statistical analysis
Statistical methods
Studies
Two dimensional
Viewing algorithms
Visualization
ISSN:0167-7055, 1467-8659
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Shrnutí:Visualizing correlations, i.e., the tendency of uncertain data values at different spatial positions to change contrarily or according to each other, allows inferring on the possible variations of structures in the data. Visualizing global correlation structures, however, is extremely challenging, since it is not clear how the visualization of complicated long‐range dependencies can be integrated into standard visualizations of spatial data. Furthermore, storing correlation information imposes a memory requirement that is quadratic in the number of spatial sample positions. This paper presents a novel approach for visualizing both positive and inverse global correlation structures in uncertain 2D scalar fields, where the uncertainty is modeled via a multivariate Gaussian distribution. We introduce a new measure for the degree of dependency of a random variable on its local and global surroundings, and we propose a spatial clustering approach based on this measure to classify regions of a particular correlation strength. The clustering performs a correlation filtering, which results in a representation that is only linear in the number of spatial sample points. Via cluster coloring the correlation information can be embedded into visualizations of other statistical quantities, such as the mean and the standard deviation. We finally propose a hierarchical cluster subdivision scheme to further allow for the simultaneous visualization of local and global correlations.
Bibliografie:istex:B9776BA1704F2BCB2766DBE38918C955C8E7CCC8
ArticleID:CGF3095
ark:/67375/WNG-5LDMWZSR-J
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03095.x