TY - GEN
T1 - A quadratically convergent proximal algorithm for nonnegative tensor decomposition
AU - Vervliet, Nico
AU - Themelis, Andreas
AU - Patrinos, Panagiotis
AU - de Lathauwer, Lieven
N1 - Funding Information:
This work was supported by the Research Foundation Flanders (FWO) via projects G086518N, G086318N, and via postdoc grant 12ZM220N; KU Leuven Internal Funds via projects C14/18/068, C16/15/059, and IDN/19/014; Fonds de la Recherche Scientifique—FNRS and the Fonds Wetenschappelijk Onderzoek—Vlaanderen under EOS project No. 30468160 (SeLMA). This research received funding from the Flemish Government under the “Onder-zoeksprogramma Artificiële Intelligentie (AI) Vlaanderen” program.
Funding Information:
This work was supported by the Research Foundation Flanders (FWO) via projects G086518N, G086318N, and via postdoc grant 12ZM220N; KU Leuven Internal Funds via projects C14/18/068, C16/15/059, and IDN/19/014; Fonds de la Recherche Scientifique-FNRS and the Fonds Wetenschappelijk Onderzoek-Vlaanderen under EOS project No. 30468160 (SeLMA). This research received funding from the Flemish Government under the “Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen” program.
Publisher Copyright:
© 2021 European Signal Processing Conference, EUSIPCO. All rights reserved.
PY - 2021/1/24
Y1 - 2021/1/24
N2 - 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 efficiency 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.
AB - 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 efficiency 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.
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U2 - 10.23919/Eusipco47968.2020.9287549
DO - 10.23919/Eusipco47968.2020.9287549
M3 - Conference contribution
AN - SCOPUS:85099277837
T3 - European Signal Processing Conference
SP - 1020
EP - 1024
BT - 28th European Signal Processing Conference, EUSIPCO 2020 - Proceedings
PB - European Signal Processing Conference, EUSIPCO
T2 - 28th European Signal Processing Conference, EUSIPCO 2020
Y2 - 24 August 2020 through 28 August 2020
ER -