High-dimensional scalar function visualization using principal parameterizations

Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many computational science and engineering disciplines. We propose a principal component-based approach to visualize such fields that accurately reflects their sensitivity to their input parameters....

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Bibliographic Details
Published in:The Visual computer Vol. 40; no. 4; pp. 2571 - 2588
Main Authors: Ballester-Ripoll, Rafael, Halter, Gaudenz, Pajarola, Renato
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer Nature B.V
Subjects:
Artificial Intelligence
Computer Graphics
Computer Science
Decomposition
Dimensional analysis
Image Processing and Computer Vision
Original Article
Parameter sensitivity
Principal components analysis
Scalars
Sensitivity analysis
Tensors
Variables
Variance analysis
Visualization
Dimensionality reduction
Tensor decompositions
Sensitivity analysis
Scientific visualization
ISSN:0178-2789, 1432-2315
Online Access:Get full text
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Summary:Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many computational science and engineering disciplines. We propose a principal component-based approach to visualize such fields that accurately reflects their sensitivity to their input parameters. The method performs dimensionality reduction on the space formed by all possible partial functions (i.e., those defined by fixing one or more input parameters to specific values), which are projected to low-dimensional parameterized manifolds such as 3D curves, surfaces, and ensembles thereof. Our mapping provides a direct geometrical and visual interpretation in terms of Sobol’s celebrated method for variance-based sensitivity analysis. We furthermore contribute a practical realization of the proposed method by means of tensor decomposition, which enables accurate yet interactive integration and multilinear principal component analysis of high-dimensional models.
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ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-023-02937-4