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Auto-weighted tensor completion and its fast algorithm
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AI
DOI：10.1016/j.patcog.2025.112880.png)
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Abstract
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The low-rank tensor completion (LRTC) problem has recently garnered substantial interest in the machine learning community, particularly within computer vision and image processing applications. Considering the significance of different singular values in low-rank tensors, the weighted tensor nuclear norm (WTNN) methods have attracted widespread attention in LRTC problems. However, most existing WTNN approaches utilize predetermined/fixed weighting schemes for singular values, thereby constraining their adaptability and performance in real-world applications. To address these limitations, we first propose an auto-weighted tensor completion (AWTC) method. Instead of using predefined and manually set weights for the low-rank tensor as in previous works, the weights here are treated as learnable variables that are automatically updated, and adaptively assigned different weights to match the singular values of the low-rank tensor. Then, to improve the computational efficiency of the AWTC model, we develop an accelerated AWTC algorithm based on approximate tensor singular value decomposition, which achieves significant computational speedup while maintaining equivalent recovery accuracy. We further develop an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) framework to implement AWTC model, and conduct a convergence analysis of the algorithm. Experimental results validated the effectiveness of the proposed method.
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