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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Vydané v:	The Visual computer Ročník 40; číslo 4; s. 2571 - 2588
Hlavní autori:	Ballester-Ripoll, Rafael, Halter, Gaudenz, Pajarola, Renato
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024 Springer Nature B.V
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Ballester-Ripoll, Rafael Pajarola, Renato Halter, Gaudenz
Author_xml	– sequence: 1 givenname: Rafael orcidid: 0000-0001-5831-2056 surname: Ballester-Ripoll fullname: Ballester-Ripoll, Rafael email: rafael.ballester@ie.edu organization: IE University – sequence: 2 givenname: Gaudenz surname: Halter fullname: Halter, Gaudenz organization: University of Zurich – sequence: 3 givenname: Renato surname: Pajarola fullname: Pajarola, Renato organization: University of Zurich
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Cites_doi	10.1006/jcom.2001.0588 10.1137/17M1160252 10.1016/j.probengmech.2013.02.002 10.1073/pnas.88.20.9107 10.1109/TVCG.2011.244 10.1111/cgf.13177 10.1109/TVCG.2010.190 10.1109/TVCG.2010.213 10.1016/j.laa.2009.07.024 10.1109/MSP.2014.2329429 10.1007/3-540-47969-4_30 10.1109/TVCG.2016.2640960 10.1109/TVCG.2014.2346321 10.1007/s10596-017-9641-4 10.1007/978-1-4899-7547-8_5 10.1111/cgf.13176 10.1109/TVCG.2011.248 10.1137/1.9781611973860 10.1002/gamm.201310004 10.1137/090752286 10.1109/TSMCB.2003.808183 10.1016/j.foodqual.2016.06.011 10.1002/9780470725184 10.1073/pnas.95.24.14190 10.1137/15M1036919 10.1109/VAST.2010.5652460 10.1109/TVCG.2007.70406 10.1137/07070111X 10.1109/VISUAL.1993.398859 10.2172/1733296 10.1016/j.ress.2008.11.012 10.1162/jocn.1991.3.1.71 10.1145/3002151.3002167
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References_xml	– reference: DubourgVSudretBDeheegerFMetamodel-based importance sampling for structural reliability analysisProbab. Eng. Mech.201333475710.1016/j.probengmech.2013.02.002 – reference: BrucknerSMoellerTResult-driven exploration of simulation parameter spaces for visual effects designIEEE Trans. Vis. Comput. Graph.20101661467147510.1109/TVCG.2010.190 – reference: OseledetsIVTensor-train decompositionSIAM J. Sci. Comput.201133522952317283753310.1137/090752286 – reference: VervlietNDebalsOSorberLLathauwerLDBreaking the curse of dimensionality using decompositions of incomplete tensors: tensor-based scientific computing in big data analysisIEEE Signal Process. Mag.2014315717910.1109/MSP.2014.2329429 – reference: OseledetsIVTyrtyshnikovETT-cross approximation for multidimensional arraysLinear Algebra Appl.201043217088256645910.1016/j.laa.2009.07.024 – reference: Ward, M.O., LeBlanc, J.T., Tipnis, R.: N-land: a graphical tool for exploring N-dimensional data. 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SubjectTerms	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
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Title	High-dimensional scalar function visualization using principal parameterizations
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