Decoupling Multivariate Functions Using Second-Order Information and Tensors

Philippe Dreesen, Jeroen De Geeter, Mariya Kamenova Ishteva

Research output: Chapter in Book/Report/Conference proceedingConference paper

7 Citations (Scopus)


The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We study decoupled representations of multivariate vector functions, which are linear combinations of univariate functions in linear combinations of the input variables. This model structure provides a description with fewer parameters, and reveals the internal workings in a simpler way, as the nonlinearities are one-to-one functions. In earlier work, a tensor-based method was developed for performing this decomposition by using first-order derivative information. In this article, we generalize this method and study how the use of second-order derivative information can be incorporated. By doing this, we are able to push the method towards more involved configurations, while preserving uniqueness of the underlying tensor decompositions. Furthermore, even for some non-identifiable structures, the method seems to return a valid decoupled representation. These results are a step towards more general data-driven and noise-robust tensor-based framework for computing decoupled function representations.

Original languageEnglish
Title of host publicationLatent Variable Analysis and Signal Separation - 14th International Conference, LVA/ICA 2018, Proceedings
EditorsSharon Gannot, Yannick Deville, Russell Mason, Mark D. Plumbley, Dominic Ward
PublisherSpringer International Publishing
Number of pages10
ISBN (Print)9783319937632
Publication statusPublished - 2 Jul 2018
Event14th International Conference on Latent Variable Analysis and Signal Separation - University of Surrey, Guilford, United Kingdom
Duration: 2 Jul 20186 Jul 2018


Conference14th International Conference on Latent Variable Analysis and Signal Separation
Abbreviated titleLVA/ICA 2018
CountryUnited Kingdom
Internet address


  • CPD
  • Function decomposition
  • Polynomial
  • Tensor
  • Tensor decomposition
  • Waring decomposition


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