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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. A sparse grid based method for generative dimensionality reduction of highdimensional data
 Journal of computational physics 309 (2016), pp.117 ISSN: 00219991 

 English 
 Journal Article 
 Fraunhofer SCAI () 
Abstract
Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a lowdimensional space to the highdimensional 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 gridbased 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 realworld 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 dimensionadaptive 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.