Low-Rank Tensor Completion via Tensor Ring with Balanced Unfolding
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Tensor completion aims to recover a multi-dimensional array from its incomplete observations. Among the existing tensor decompositions, tensor ring (TR) is special for its cyclic structure. Due to this cycle, TR unfoldings may capture more global correlations than those of other decompositions in some applications. In this paper, we propose a novel low rank tensor completion based on TR with balanced unfolding, which generalizes the characteristic of balance in matrix completion. We first develop a sampling theorem for low rank TR completion, which suggests a class of balanced TR unfoldings. Using these balanced unfoldings, a new optimization model for tensor completion can be formed. The alternating direction method of multipliers (ADMM) is used to solve this optimization problem, which is called TRBU. Both the computational complexity and convergence are analyzed to show its performance improvement. The experiments on synthetic data verify the correctness of theoretic analysis, and the numerical results of real-world data demonstrate that the proposed method outperforms the state-of-the-art ones in terms of recovery accuracy.
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