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International Conference on Latent Variable Analysis and Signal Separation

LVA/ICA 2015: Latent Variable Analysis and Signal Separation pp 14–21Cite as

Block-Decoupling Multivariate Polynomials Using the Tensor Block-Term Decomposition

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9237))

Abstract

We present a tensor-based method to decompose a given set of multivariate functions into linear combinations of a set of multivariate functions of linear forms of the input variables. The method proceeds by forming a three-way array (tensor) by stacking Jacobian matrix evaluations of the function behind each other. It is shown that a block-term decomposition of this tensor provides the necessary information to block-decouple the given function into a set of functions with small input-output dimensionality. The method is validated on a numerical example.

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Acknowledgments

This work was supported in part by the Fund for Scientific Research (FWO-Vlaanderen), by the Flemish Government (Methusalem), by the Belgian Government through the Inter-university Poles of Attraction (IAP VII) Program, by the ERC Advanced Grant SNLSID under contract 320378, by the ERC Advanced Grant BIOTENSORS under contract 339804, by the ERC Starting Grant SLRA under contract 258581, by the Research Council KU Leuven: CoE PFV/10/002 (OPTEC), by FWO projects G.0830.14N, G.0881.14N, and G.0280.15N and by the Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO II, Dynamical systems, control and optimization, 2012–2017). Mariya Ishteva is an FWO Pegasus Marie Curie Fellow.

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Authors and Affiliations

  1. Vrije Universiteit Brussel (VUB), Brussels, Belgium

    Philippe Dreesen, Thomas Goossens, Mariya Ishteva & Johan Schoukens

  2. Department of Electrical Engineering (ESAT/STADIUS) and iMinds Medical IT, KU Leuven, Leuven, Belgium

    Thomas Goossens & Lieven De Lathauwer

  3. KU Leuven Campus Kortrijk, Kortrijk, Belgium

    Lieven De Lathauwer

Authors
  1. Philippe Dreesen
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  2. Thomas Goossens
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  3. Mariya Ishteva
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  4. Lieven De Lathauwer
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  5. Johan Schoukens
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Corresponding author

Correspondence to Philippe Dreesen .

Editor information

Editors and Affiliations

  1. Inria, Villers-les-Nancy, France

    Emmanuel Vincent

  2. Tel Aviv University, Tel-Aviv, Israel

    Arie Yeredor

  3. Technical University of Libere, Liberec, Czech Republic

    Zbyněk Koldovský

  4. The Czech Academy of Sciences, Prague, Czech Republic

    Petr Tichavský

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© 2015 Springer International Publishing Switzerland

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Dreesen, P., Goossens, T., Ishteva, M., De Lathauwer, L., Schoukens, J. (2015). Block-Decoupling Multivariate Polynomials Using the Tensor Block-Term Decomposition. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-22482-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22481-7

  • Online ISBN: 978-3-319-22482-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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