SFBS: a Forward-Backward Splitting algorithm for constrained tensor decomposition
Résumé
Tensors (multi-way arrays) and constrained tensor decomposition are very practical in various applications. The existing constrained decomposition algorithms, which are based on Alternating Direction Method of Multipliers (ADMM) or proximal methods, suffer either from a lack of complete convergence guarantee or from the lack of expected accuracy. In this paper, we propose a constrained decomposition algorithm, called SFBS, which stands for ``Simple Forward-Backward Splitting'' and is based on a particular proximal method to handle constraints. SFBS is theoretically and practically ahead compared to the state-of-the-art, since (i) not only SFBS achieves state-of-the-art performances, but also has a complete convergence guarantee, unlike ADMM-based algorithms; (ii) SFBS is much more robust against additive noise and computationally less expensive; (iii) unlike some existing algorithms, SFBS requires to adjust fewer hyperparameters, which are easy to set according to the convergence condition.
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