Algebraic and optimization based algorithms for multivariate regression using symmetric tensor decomposition

Stijn Hendrikx, Martijn Boussé, Nico Vervliet, Lieven De Lathauwer


Multivariate regression is an important task in domains such as machine learning and statistics. We cast this regression problem as a linear system with a solution that is a vectorized symmetric low-rank tensor. We show that the structure of the data and the decomposition can be exploited to obtain efficient optimization methods. Furthermore, we show that an algebraic algorithm can be derived even when the number of given data points is low. We illustrate the performance of our regression model using a real-life dataset from materials sciences.

Code description

This package provides the algorithms, experiment files and auxiliary files for the paper on multivariate regression using symmetric tensor decompositions.


S. Hendrikx, M. Boussé, N. Vervliet, L. De Lathauwer, "Algebraic and Optimization Based Algorithms for Multivariate Regression Using Symmetric Tensor Decomposition," 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2019), pp. 475-479, Dec. 2019.

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This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from