Abstract
In this paper, we analyse and solve a source separation problem based on a mixing model that is nonlinear and non-invertible at the space of mixtures. The model is relevant considering it may represent the data obtained from ion-selective electrode arrays. We apply a new approach for solving the problems of local stability of the recurrent network previously used in the literature, which allows for a wider range of source concentration. In order to achieve this, we utilize a second-order recurrent network which can be shown to be locally stable for all solutions. Using this new network and the priors that chemical sources are continuous and smooth, our proposal performs better than the previous approach.
The authors would like to thank FAPESP, CNPq, CNRS and ERC project 2012-ERC-AdG-320684 CHESS for the funding.
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References
Ando, R.A.: Blind Source Separation in the Context of Polynomial Mixtures. Master’s thesis, School of Electrical and Computer Engeneering, University of Campinas (2013)
Comon, P., Jutten, C.: Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic press, USA (2010)
Duarte, L.T., Jutten, C.: Design of smart ion-selective electrode arrays based on source separation through nonlinear independent component analysis. Oil Gas Sci. Technol.-Rev. d’IFP Energies Nouvelles 69(2), 293–306 (2014)
Hosseini, S., Deville, Y.: Blind separation of linear-quadratic mixtures of real sources using a recurrent structure. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2687, pp. 241–248. Springer, Heidelberg (2003)
Hyvärinen, A., Pajunen, P.: Nonlinear independent component analysis: existence and uniqueness results. Neural Netw. 12(3), 429–439 (1999)
Jutten, C., Karhunen, J.: Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures. Int. J. Neural Syst. 14(05), 267–292 (2004)
Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Trans. Sig. Process. 47(10), 2807–2820 (1999)
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Baptista, D.F.F., Ando, R.A., Duarte, L.T., Jutten, C., Attux, R. (2015). Theoretical Studies and Algorithms Regarding the Solution of Non-invertible Nonlinear Source Separation. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_36
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DOI: https://doi.org/10.1007/978-3-319-22482-4_36
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