Low Rank Tensor Completion via Adaptive ADMM

TL;DR

This paper introduces a novel low-rank tensor completion algorithm based on ADMM, which improves convergence speed and accuracy over existing methods by reformulating the nuclear norm minimization problem.

Contribution

It extends matrix completion techniques to tensors using an adaptive ADMM framework with closed-form solutions, enhancing efficiency and performance.

Findings

Outperforms state-of-the-art tensor completion methods in NMSE

Uses adaptive penalty updates to accelerate convergence

Initialization with existing solutions further improves results

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.