🤖 AI Summary
This study addresses the problem of partially observed low-rank tensor completion, a high-dimensional generalization of matrix completion. Building upon the nuclear norm minimization framework, the authors propose an improved adaptive alternating direction method of multipliers (ADMM) algorithm that incorporates an over-relaxation mechanism and a dynamic penalty parameter update strategy. This formulation efficiently decomposes the original problem into subproblems amenable to parallel computation and leverages closed-form proximal operators to enable rapid iterations. The proposed method achieves significantly accelerated convergence and enhanced completion accuracy, outperforming state-of-the-art approaches in terms of normalized mean squared error (NMSE). Furthermore, when combined with an advanced initialization strategy, both its performance and convergence speed are further improved.
📝 Abstract
We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN) minimization-based low-rank TC paradigm, by leveraging the alternating direction method of multipliers (ADMM) optimization framework. To that extend the original NN minimization problem is reformulated into multiple subproblems, which are then solved iteratively via closed-form proximal operators, making use of over-relaxation and an adaptive penalty parameter update scheme, to further speed up convergence and improve the overall performance of the method. Simulation results demonstrate the superior performance of the new method in terms of normalized mean square error (NMSE), compared to the conventional state-of-the-art (SotA) techniques, including NN minimization approaches, as well as a mixture of the latter with a matrix factorization approach, while its convergence can be significantly improved by initializing the algorithm with the solution of the SotA.