gpICA: a novel nonlinear ICA algorithm using geometric linearization

Authors:
Thang Viet Nguyen;Jagdish Chandra Patra;Sabu Emmanuel
Affiliations:
School of Computer Engineering, Nanyang Technological University, Singapore;School of Computer Engineering, Nanyang Technological University, Singapore;School of Computer Engineering, Nanyang Technological University, Singapore
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2007

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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.