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Joint Nonnegative Matrix Factorization for Underdetermined Blind Source Separation in Nonlinear Mixtures

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Latent Variable Analysis and Signal Separation (LVA/ICA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10891))

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Abstract

An approach is proposed for underdetermined blind separation of nonnegative dependent (overlapped) sources from their nonlinear mixtures. The method performs empirical kernel maps based mappings of original data matrix onto reproducible kernel Hilbert spaces (RKHSs). Provided that sources comply with probabilistic model that is sparse in support and amplitude nonlinear underdetermined mixture model in the input space becomes overdetermined linear mixture model in RKHS comprised of original sources and their mostly second-order monomials. It is assumed that linear mixture models in different RKHSs share the same representation, i.e. the matrix of sources. Thus, we propose novel sparseness regularized joint nonnegative matrix factorization method to separate sources shared across different RKHSs. The method is validated comparatively on numerical problem related to extraction of eight overlapped sources from three nonlinear mixtures.

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Acknowledgments

This work has been supported in part by the Grant IP-2016-06-5253 funded by Croatian Science Foundation and in part by the European Regional Development Fund under the grant KK.01.1.1.01.0009 (DATACROSS).

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Authors and Affiliations

  1. Division of Electronics, Ruđer Bošković Institute, Bijenička cesta 54, 10000, Zagreb, Croatia

    Ivica Kopriva

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  1. Ivica Kopriva
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Correspondence to Ivica Kopriva .

Editor information

Editors and Affiliations

  1. Paul Sabatier University, Toulouse, France

    Yannick Deville

  2. Bar-Ilan University, Ramat Gan, Israel

    Sharon Gannot

  3. University of Surrey, Guildford, United Kingdom

    Russell Mason

  4. University of Surrey, Guildford, United Kingdom

    Mark D. Plumbley

  5. University of Surrey, Guildford, United Kingdom

    Dominic Ward

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Kopriva, I. (2018). Joint Nonnegative Matrix Factorization for Underdetermined Blind Source Separation in Nonlinear Mixtures. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-93764-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93763-2

  • Online ISBN: 978-3-319-93764-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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