Computation of the regularized canonical polyadic decomposition of tensors using the accelerated proximal gradient with momentum
Le calcul de la décomposition polyadique canonique régularisée des tenseurs en utilisant le gradient proximal accéléré avec momentum
Résumé
Tensors may be seen as multidimensional arrays that generalize vectors and matrices to more than two dimensions. Among tensor decompositions, we are especially interested in the Canonical Polyadic (CP) tensor decomposition, which is important in numerous real-world applications, for its uniqueness and ease of interpretation of its factor matrices. In this research, we propose a new Canonical Polyadic (CP) model based on the Accelerated Proximal Gradient (PG) algorithm and through the introduction of a regularization function that incorporates the previous iterations; using a new strategy capable of efficiently conducting this incorporation. Simulation results demonstrate the better performance of the proposed approach in terms of accuracy and rapidity compared to other algorithms in the literature, especially when the swamp phenomenon occurs.
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