Two Factors Update for Canonical Polyadic Decomposition

Anastasia Sozykina, Valentin Leplat, Igor Vorona, Salman Ahmadi-Asl, ANH-HUY PHAN

Keywords: Tensor Decomposition, Canonical Polyadic Decomposition, Non-Convex Non-Smooth Optimisation

Abstract: The current alternating optimization algorithms for canonical polyadic (CP) tensor decomposition face various challenges such as redundant update steps and the robustness of optimization when dealing with linearly dependent factor matrices. These concerns often result in prolonged iterations without substantial progress in the decomposition process. In response to these challenges, our paper introduces two novel optimization algorithms for computing CP decompositions relying on the update of two factor matrices simultaneously. We assess the performance of our algorithm by conducting thorough numerical experiments involving both synthetic and real-world data tensors. Through these experiments, we demonstrate the efficiency and benefits of our proposed approach.

Submission Number: 18