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Pré-Publication, Document De Travail Année : 2020

FBS4: A Forward-Backward Splitting algorithm for constrained tensor decomposition

Résumé

Tensors (multi-way arrays) are very practical in various applications such as chemometrics, text mining, medical image and signal processing, where desired parameters are estimated by tensor decomposition. It has been shown that constrained tensor decomposition performs better than unconstrained in parameter identification problems. Most tensor decomposition algorithms are based on Alternating Least Squares (ALS), and for constrained decomposition it is needed to solve a constrained minimization in each step of ALS. Over the past decade, some algorithms based on ALS have been proposed for constrained (mostly non-negative) tensor decomposition, and applied Alternating Direction Method of Multipliers (ADMM) or proximal methods to handle the constraint. Although ADMM based method performs efficiently in various cases, there is no convergence guarantee for this method in case of non-convex constraint. On the other hand, proximal based methods proposed so far suffer from lack of expected accuracy in the decomposition, while there is a convergence proof for these kinds of methods even in case of non-convexity. In this paper, an algorithm is proposed based on ALS for constrained tensor decomposition, which utilizes a particular proximal method called Forward-Backward Splitting to handle the constraint. We call this algorithm FBS4, which stands for "Forward-Backward Splitting with Smart initialization for tensor CP decompositions under non-negativity, Sparsness or Simplex constraints". FBS4 is theoretically one step ahead compared to ADMM-based methods, since (i) the provided convergence analysis of FBS4 holds true for both convex and non-convex constraints such as sparsity; (ii) in practice FBS4 enables to manage a large range of constraints such as non-negativity, simplex set and sparsity; (iii) computer results show that FBS4 achieves state-of-the-art performances; (iv) FBS4 algorithm is simpler and faster compared to other algorithms based on proximal approaches.
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Dates et versions

hal-02929348 , version 1 (03-09-2020)
hal-02929348 , version 2 (10-02-2023)

Identifiants

  • HAL Id : hal-02929348 , version 1

Citer

Elaheh Sobhani, Pierre Comon, Christian Jutten, Massoud Babaie-Zadeh. FBS4: A Forward-Backward Splitting algorithm for constrained tensor decomposition. 2020. ⟨hal-02929348v1⟩
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