Low Rank Tensor Completion via Adaptive ADMM
Niclas Führling, Getuar Rexhepi, Giuseppe Thadeu Freitas de Abreu
TLDR
This paper introduces an adaptive ADMM algorithm for low-rank tensor completion, outperforming state-of-the-art methods.
Key contributions
- Proposes a novel low-rank tensor completion method using an adaptive ADMM framework.
- Reformulates nuclear norm minimization into subproblems solved by closed-form proximal operators.
- Incorporates over-relaxation and adaptive penalty updates to accelerate convergence and improve performance.
- Demonstrates superior performance in NMSE compared to conventional state-of-the-art techniques.
Why it matters
This paper offers a more efficient and accurate solution for low-rank tensor completion, a critical task in various data science applications. Its adaptive ADMM approach significantly improves upon existing methods, providing faster convergence and better performance. This advancement can lead to more robust data recovery and analysis.
Original 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.
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