LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation

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LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation
Title:
LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation
Journal Title:
Proceedings of the AAAI Conference on Artificial Intelligence
Publication Date:
25 March 2024
Citation:
Xu, Z., Zhang, Y., Ma, C., Yan, Y., Peng, Z., Xie, S., Wu, S., & Yang, X. (2024). LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation. Proceedings of the AAAI Conference on Artificial Intelligence, 38(14), 16228–16236. https://doi.org/10.1609/aaai.v38i14.29557
Abstract:
A fundamental task in the realms of computer vision, Low-Rank Matrix Recovery (LRMR) focuses on the inherent low-rank structure precise recovery from incomplete data and/or corrupted measurements given that the rank is a known prior or accurately estimated. However, it remains challenging for existing rank estimation methods to accurately estimate the rank of an ill-conditioned matrix. Also, existing LRMR optimization methods are heavily dependent on the chosen parameters, and are therefore difficult to adapt to different situations. Addressing these issues, A novel LEarning-based low-rank matrix recovery with Rank Estimation (LERE) is proposed. More specifically, considering the characteristics of the Gerschgorin disk's center and radius, a new heuristic decision rule in the Gerschgorin Disk Theorem is significantly enhanced and the low-rank boundary can be exactly located, which leads to a marked improvement in the accuracy of rank estimation. According to the estimated rank, we select row and column sub-matrices from the observation matrix by uniformly random sampling. A 17-iteration feedforward-recurrent-mixed neural network is then adapted to learn the parameters in the sub-matrix recovery processing. Finally, by the correlation of the row sub-matrix and column sub-matrix, LERE successfully recovers the underlying low-rank matrix. Overall, LERE is more efficient and robust than existing LRMR methods. Experimental results demonstrate that LERE surpasses state-of-the-art (SOTA) methods. The code for this work is accessible at https://github.com/zhengqinxu/LERE.
License type:
Publisher Copyright
Funding Info:
There was no specific funding for the research done
Description:
ISSN:
2159-5399
2374-3468
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