Paper ID sheet UCL-INMA-2018.01

Title

Variable projection applied to block term decomposition of higher-order tensors

Authors

Guillaume Olikier, P.-A. Absil, Lieven De Lathauwer

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.

Key words

numerical multilinear algebra; higher-order tensor; block term decomposition; variable projection method; Riemannian manifold; Riemannian optimization

Status

Proceedings of the 14th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2018), to appear

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• Publisher's version: doi:10.1007/978-3-319-93764-9_14
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