Robust to Rank Selection: Low-Rank Sparse Tensor-Ring Completion.

Area of Science:

• Data Science
• Numerical Analysis
• Machine Learning

Background:

• Tensor-ring (TR) decomposition is effective for high-order tensor representation and low-rank tensor completion.
• Existing TR-based methods often degrade when the chosen rank exceeds the true tensor rank.

Purpose of the Study:

• To propose a novel low-rank sparse TR completion method.
• To address the rank-overestimation issue in conventional TR completion.

Main Methods:

• Imposing Frobenius norm regularization on the latent space of TR decomposition.
• Utilizing Kronecker-basis-representation (KBR)-based sparsity.
• Optimization via block coordinate descent (BCD) algorithm.
• Modified TR decomposition for initialization.

Main Results:

• Theoretically established the method's ability to exploit low rankness and KBR-based sparsity.
• Experimental results show superior performance over conventional TR-based and state-of-the-art methods.
• Demonstrated robustness to increased TR-rank selection.

Conclusions:

• The proposed low-rank sparse TR completion method offers improved accuracy and robustness.
• It effectively handles tensor completion even with higher rank estimations.