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.
| Original language | English |
|---|---|
| Article number | 5876340 |
| Pages (from-to) | 4478-4482 |
| Number of pages | 5 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 59 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2011 Sep 1 |
| Externally published | Yes |
Fingerprint
Keywords
- Identifiability
- independent subspace analysis
- non-Gaussian component analysis
- projection pursuit
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Signal Processing
Cite this
Uniqueness of non-gaussianity-based dimension reduction. / Theis, Fabian J.; Kawanabe, Motoaki; Muller, Klaus.
In: IEEE Transactions on Signal Processing, Vol. 59, No. 9, 5876340, 01.09.2011, p. 4478-4482.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Uniqueness of non-gaussianity-based dimension reduction
AU - Theis, Fabian J.
AU - Kawanabe, Motoaki
AU - Muller, Klaus
PY - 2011/9/1
Y1 - 2011/9/1
N2 - 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.
AB - 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.
KW - Identifiability
KW - independent subspace analysis
KW - non-Gaussian component analysis
KW - projection pursuit
UR - http://www.scopus.com/inward/record.url?scp=80051716561&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051716561&partnerID=8YFLogxK
U2 - 10.1109/TSP.2011.2159600
DO - 10.1109/TSP.2011.2159600
M3 - Article
AN - SCOPUS:80051716561
VL - 59
SP - 4478
EP - 4482
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 9
M1 - 5876340
ER -