Uniqueness of non-gaussianity-based dimension reduction

Fabian J. Theis, Motoaki Kawanabe, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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 languageEnglish
Article number5876340
Pages (from-to)4478-4482
Number of pages5
JournalIEEE Transactions on Signal Processing
Volume59
Issue number9
DOIs
Publication statusPublished - 2011 Sept

Bibliographical note

Funding Information:
Manuscript received July 29, 2010; revised November 22, 2010, March 03, 2011, and May 26, 2011; accepted May 27, 2011. Date of publication June 16, 2011; date of current version August 10, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Kainam Thomas Wong. F. J. Theis gratefully acknowledges partial financial supported by the Helmholtz Alliance on Systems Biology (project “CoReNe”). M. Kawanabe and K.-R. Müller acknowledge the THESEUS project (01MQ07018) funded by the German Federal Ministry of Economics and Technology. K.-R. Müller also acknowledges general support by the BMBF and DFG.

Keywords

  • Identifiability
  • independent subspace analysis
  • non-Gaussian component analysis
  • projection pursuit

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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