A nonlinear source separation approach for the Nicolsky-Eisenman model

In previous works [7, 8], we proposed source separation methods for a simplified version of the Nicolsky-Eisenman (NE) model, which is related to a chemical sensing application. In the present paper, we provide a method able to deal with the complete NE model. Basically, such a model can be seen as a composition of a non-diagonal nonlinear transformation followed by a diagonal nonlinear transformation, i.e. a set of component-wise functions. The basic idea behind the developed technique is to estimate the parameters of these two stages in a separate fashion by using a prior knowledge of the sources, namely the fact that one of the sources is constant during a certain period of time. Simulations attest the viability of the proposed technique.

[1]  C. Jutten,et al.  Improving semiconductor-based chemical sensor arrays using advanced algorithms for blind source separation , 2004, ISA/IEEE Sensors for Industry Conference, 2004. Proceedings the.

[2]  C. Jutten,et al.  A Mutual Information Minimization Approach for a Class of Nonlinear Recurrent Separating Systems , 2007, 2007 IEEE Workshop on Machine Learning for Signal Processing.

[3]  Christian Jutten,et al.  Blind Source Separation of a Class of Nonlinear Mixtures , 2007, ICA.

[4]  Yoshio Umezawa,et al.  Potentiometric Selectivity Coefficients of Ion-Selective Electrodes. Part I. Inorganic Cations (Technical Report) , 2000 .

[5]  Aapo Hyvärinen,et al.  Nonlinear independent component analysis: Existence and uniqueness results , 1999, Neural Networks.

[6]  Juha Karhunen,et al.  Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures , 2004, Int. J. Neural Syst..

[7]  Igor Vajda,et al.  Estimation of the Information by an Adaptive Partitioning of the Observation Space , 1999, IEEE Trans. Inf. Theory.

[8]  Christian Jutten,et al.  A geometric approach for separating post non-linear mixtures , 2002, 2002 11th European Signal Processing Conference.

[9]  Yannick Deville,et al.  Blind Separation of Linear-Quadratic Mixtures of Real Sources Using a Recurrent Structure , 2009, IWANN.

[10]  João Marcos Travassos Romano,et al.  Blind Search for Optimal Wiener Equalizers Using an Artificial Immune Network Model , 2003, EURASIP J. Adv. Signal Process..

[11]  Yannick Deville,et al.  Temporal and time-frequency correlation-based blind source separation methods. Part I: Determined and underdetermined linear instantaneous mixtures , 2007, Signal Process..

[12]  Fernando José Von Zuben,et al.  Learning and optimization using the clonal selection principle , 2002, IEEE Trans. Evol. Comput..