{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/visualization-of-high-dimensional-scalar","title":"Visualization of High-dimensional Scalar Functions Using Principal Parameterizations","arxiv_id":"1809.03618","date":"2018-09-11","proceeding":null,"authors":["Rafael Ballester-Ripoll","Renato Pajarola"],"abstract":"Insightful visualization of multidimensional scalar fields, in particular\nparameter spaces, is key to many fields in computational science and\nengineering. We propose a principal component-based approach to visualize such\nfields that accurately reflects their sensitivity to input parameters. The\nmethod performs dimensionality reduction on the vast $L^2$ Hilbert space formed\nby all possible partial functions (i.e., those defined by fixing one or more\ninput parameters to specific values), which are projected to low-dimensional\nparameterized manifolds such as 3D curves, surfaces, and ensembles thereof. Our\nmapping provides a direct geometrical and visual interpretation in terms of\nSobol's celebrated method for variance-based sensitivity analysis. We\nfurthermore contribute a practical realization of the proposed method by means\nof tensor decomposition, which enables accurate yet interactive integration and\nmultilinear principal component analysis of high-dimensional models.","url_abs":"http://arxiv.org/abs/1809.03618v1","url_pdf":"http://arxiv.org/pdf/1809.03618v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"visualization-of-high-dimensional-scalar","repo_url":"https://github.com/rballester/ttpca","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"sensitivity","task_name":"Sensitivity"},{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}