Variable Projection Applied to Block Term Decomposition of Higher-Order Tensors

Olikier, Guillaume;Absil, Pierre-Antoine;De Lathauwer, Lieven
(2018) LVA ICA 2018 — Location: Guildford, UK (2.July.2018)

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Authors
  • Olikier, GuillaumeUCLouvain
    Author
  • Absil, Pierre-AntoineUCLouvain
    Author
  • De Lathauwer, LievenDepartment of Electrical Engineering (ESAT)KU Leuven Belgium
    Author
Abstract
Higher-order tensors have become popular in many areas of applied mathematics such as statistics, scientific computing, signal processing or machine learning, notably thanks to the many possible ways of decomposing a tensor. In this paper, we focus on the best approximation in the least-squares sense of a higher-order tensor by a block term decomposition. Using variable projection, we express the tensor approximation problem as a minimization of a cost function on a Cartesian product of Stiefel manifolds. The effect of variable projection on the Riemannian gradient algorithm is studied through numerical experiments.
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Olikier, G., Absil, P.-A., & De Lathauwer, L. (2018). Variable Projection Applied to Block Term Decomposition of Higher-Order Tensors. Latent Variable Analysis and Signal Separation : Lecture Notes in Computer Science, p. 139-148. https://doi.org/10.1007/978-3-319-93764-9_14