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Uniqueness of non-gaussianity-based dimension reduction

 
: Theis, F.J.; Kawanabe, M.; Müller, K.-R.

:

IEEE transactions on signal processing 59 (2011), No.9, pp.4478-4482
ISSN: 0096-3518
ISSN: 0018-9278
ISSN: 0096-1620
ISSN: 1053-587X
English
Journal Article
Fraunhofer FIRST ()

Abstract
Dimension reduction is a key step in preprocessing large-scale data sets. A recently proposed method named non-Gaussian component analysis searches for a projection onto the non-Gaussian part of a given multivariate recording, which is a generalization of the deflationary projection pursuit model. In this contribution, we discuss the uniqueness of the subspaces of such a projection. We prove that a necessary and sufficient condition for uniqueness is that the non-Gaussian signal subspace is of minimal dimension. Furthermore, we propose a measure for estimating this minimal dimension and illustrate it by numerical simulations. Our result guarantees that projection algorithms uniquely recover the underlying lower dimensional data signals.

: http://publica.fraunhofer.de/documents/N-189371.html