A quadratically convergent proximal algorithm for nonnegative tensor decomposition

Nico Vervliet, Andreas Themelis, Panos Patrinos, Lieven De Lathauwer


The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic decomposition (CPD) is unique under mild conditions, including prior knowledge such as nonnegativity can facilitate interpretation of the components. Inspired by the effectiveness and effciency of Gauss–Newton (GN) for unconstrained CPD, we derive a proximal, semismooth GN type algorithm for nonnegative tensor factorization. Global convergence to local minima is achieved via backtracking on the forward-backward envelope function. If the algorithm converges to a global optimum, we show that Q-quadratic rates are obtained in the exact case. Such fast rates are verified experimentally, and we illustrate that using the GN step significantly reduces number of (expensive) gradient computations compared to proximal gradient descent.

Code description

This package provides the implementation of the proximal Gauss-Newton type algorithm for computing the nonnegative canonical polyadic decomposition of a tensor as proposed in the paper on the proximal Gauss-Newton method. Experiment files reproducing the results from Section VI are included as well.


N. Vervliet, A. Themelis, P. Patrinos, L. De Lathauwer, "A quadratically convergent proximal algorithm for nonnegative tensor decomposition," 2020 28th European Signal Processing Conference, EUSIPCO, pp. 1020-1024, Jan. 2021.

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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 https://www.tensorlabplus.net.