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  • Research Article
  • Open Access

gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization

  • 1Email author,
  • 1 and
  • 1
EURASIP Journal on Advances in Signal Processing20062007:031951

  • Received: 30 September 2005
  • Accepted: 11 June 2006
  • Published:


A new geometric approach for nonlinear independent component analysis (ICA) is presented in this paper. Nonlinear environment is modeled by the popular post nonlinear (PNL) scheme. To eliminate the nonlinearity in the observed signals, a novel linearizing method named as geometric post nonlinear ICA (gpICA) is introduced. Thereafter, a basic linear ICA is applied on these linearized signals to estimate the unknown sources. The proposed method is motivated by the fact that in a multidimensional space, a nonlinear mixture is represented by a nonlinear surface while a linear mixture is represented by a plane, a special form of the surface. Therefore, by geometrically transforming the surface representing a nonlinear mixture into a plane, the mixture can be linearized. Through simulations on different data sets, superior performance of gpICA algorithm has been shown with respect to other algorithms.


  • Information Technology
  • Special Form
  • Quantum Information
  • Superior Performance
  • Independent Component Analysis

Authors’ Affiliations

School of Computer Engineering, Nanyang Technological University, 639798, Singapore


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© Nguyen et al. 2007