Blind Separation of a Class of Nonlinear ICA Models

Eriksson, Jan; Koivunen, Visa

doi:10.1109/iscas.2005.1465979

Cited by 14 publications

(24 citation statements)

References 11 publications

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“…Hence, in general, non-linear mixing models with no particular a priori assumptions are affected by a strong nonuniqueness (Jutten & Herault, 1991;Eriksson & Koivunen, 2002;Theis & Gruber, 2005 , the random variables 1 y and 2 y are still independent but are Gaussian distributed, so they cannot be separated (see Jutten & Karhunen, 2003). In fact the Jacobian J of this transformation is: ( ) …”

Section: The Case Of Nonlinear Mixing Modelmentioning

confidence: 99%

Flexible Blind Signal Separation in the Complex Domain

Scarpiniti¹,

Vigliano

Parisi

et al. 2009

Complex-Valued Neural Networks

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This chapter aims at introducing an Independent Component Analysis (ICA) approach to the separation of linear and nonlinear mixtures in complex domain. Source separation is performed by an extension of the INFOMAX approach to the complex environment. The neural network approach is based on an adaptive activation function, whose shape is properly modified during learning. Different models have been used to realize complex nonlinear functions for the linear and the nonlinear environment. In nonlinear environment the nonlinear functions involved during the learning are implemented by the so-called "splitting functions", working on the real and the imaginary part of the signal. In linear environment instead, the "generalized splitting function" which perform a more complete representation of complex function is used. Moreover a simple adaptation algorithm is derived and several experimental results are shown to demonstrate the effectiveness of the proposed method.

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Section: The Case Of Nonlinear Mixing Modelmentioning

confidence: 99%

Flexible Blind Signal Separation in the Complex Domain

Scarpiniti¹,

Vigliano

Parisi

et al. 2009

Complex-Valued Neural Networks

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“…Separation of nonlinear mixtures, too, has already been addressed by a few authors [3,4,5,6,7,8,9,10]. In many applications, it is unreasonable to assume that the mixtures are linear because the underlying natural processes are inherently nonlinear.…”

Section: Introductionmentioning

confidence: 99%

“…Hence indeterminacy reduction might be considered as an objective. Generally speaking, constraints such as additional prior information on sources or mixture model make the problem well-posed [3,4,11]. As an example, Post Non-Linear (PNL) mixtures have already been shown to be separable [8,12].…”

Section: Introductionmentioning

confidence: 99%

Blind separation of bilinear mixtures using mutual information minimization

Mokhtari

Babaie‐Zadeh

Jutten

2009

2009 IEEE International Workshop on Machine Learning for Signal Processing

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In this paper an approach for blind source separation in bilinear (or linear quadratic) mixtures is presented. The proposed algorithm employs the same recurrent structure as [Hosseini and Deville, 2003] for separating these mixtures. However, instead of maximal likelihood, our algorithm is based on minimizing the mutual information of the outputs for recovering the independent components. Simulation results show the efficiency of the proposed algorithm.

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“…For example, a conformal mapping is assumed in [31]. First published in [35], more general results concerning identifiability of a large class of nonlinearities satisfying an addition theorem have been pointed out recently in [21], [34]. Other structures have been introduced; the postnonlinear one is probably one of the most popular [45], [32], [36], [22], [5], [4], [6].…”

Section: Introductionmentioning

confidence: 99%

“…First published in [35], more general results concerning identifiability of a large class of nonlinearities satisfying an addition theorem have been pointed out recently in [21], [34]. Other structures have been introduced; the postnonlinear one is probably one of the most popular [45], [32], [36], [22], [5], [4], [6]. On the other hand, the case of sources in a discrete or finite alphabet has been considered for long [37], [47], [23], [25] and the strength of the discrete sources assumption has been recognized.…”

Section: Introductionmentioning

confidence: 99%

Inversion of Polynomial Systems and Separation of Nonlinear Mixtures of Finite-Alphabet Sources

Castella

2008

IEEE Trans. Signal Process.

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To cite this version:Marc Castella. Inversion of polynomial systems and separation of nonlinear mixtures of finite-alphabet sources. IEEE Abstract-In this contribution, Multi-Input Multi-Output (MIMO) mixing systems are considered, which are instantaneous and nonlinear but polynomial. We first address the problem of invertibility, searching the inverse in the class of polynomial systems. It is shown that Groebner bases techniques offer an attractive solution for testing the existence of an exact inverse and computing it.By noticing that any nonlinear mapping can be interpolated by a polynomial on a finite set, we tackle the general nonlinear case. Relying on a finite alphabet assumption of the input source signals, theoretical results on polynomials allow us to represent nonlinear systems as linear combinations of a finite set of monomials. We then generalize the first results to give a condition for the existence of an exact nonlinear inverse. The proposed method allows to compute this inverse in polynomial form.In the light of the previous results, we go further to the blind source separation problem. It is shown that for sources in a finite alphabet, the nonlinear problem is tightly connected with both problems of underdetermination and of dependent sources. We concentrate on the case of two binary sources, for which an easy solution can be found. By simulation, this solution is compared to techniques borrowed from classification methods.

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Blind Separation of a Class of Nonlinear ICA Models

Cited by 14 publications

References 11 publications

Flexible Blind Signal Separation in the Complex Domain

Flexible Blind Signal Separation in the Complex Domain

Blind separation of bilinear mixtures using mutual information minimization

Inversion of Polynomial Systems and Separation of Nonlinear Mixtures of Finite-Alphabet Sources

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