A sparse grid based method for generative dimensionality reduction of high-dimensional data
A sparse grid based method for generative dimensionality reduction of high-dimensional data
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dc.contributor.author | Bohn, Bastian | |
dc.contributor.author | Garcke, Jochen | |
dc.contributor.author | Griebel, Michael | |
dc.date.accessioned | 2024-08-21T09:00:27Z | |
dc.date.available | 2024-08-21T09:00:27Z | |
dc.date.issued | 11.2015 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/11893 | |
dc.description.abstract | Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed. | en |
dc.format.extent | 30 | |
dc.language.iso | eng | |
dc.relation.ispartofseries | INS Preprints ; 1514 | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Generative models | |
dc.subject | Machine learning | |
dc.subject | Sparse grids | |
dc.subject | Dimensionality reduction | |
dc.subject | Numerical simulation data | |
dc.subject | Car-crash analysis | |
dc.subject.ddc | 510 Mathematik | |
dc.subject.ddc | 518 Numerische Analysis | |
dc.title | A sparse grid based method for generative dimensionality reduction of high-dimensional data | |
dc.type | Preprint | |
dc.publisher.name | Institut für Numerische Simulation (INS) | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.relation.doi | https://doi.org/10.1016/j.jcp.2015.12.033 | |
ulbbn.pubtype | Zweitveröffentlichung | |
dcterms.bibliographicCitation.url | https://ins.uni-bonn.de/publication/preprints |
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