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gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 031951 (2006) Cite this article

Abstract

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.

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Authors and Affiliations

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

    Thang Viet Nguyen, Jagdish Chandra Patra & Sabu Emmanuel

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  1. Thang Viet Nguyen
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  2. Jagdish Chandra Patra
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  3. Sabu Emmanuel
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Correspondence to Thang Viet Nguyen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nguyen, T.V., Patra, J.C. & Emmanuel, S. gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization. EURASIP J. Adv. Signal Process. 2007, 031951 (2006). https://doi.org/10.1155/2007/31951

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