Double-Weighted Low-Rank Matrix Recovery Based on Rank Estimation

Xu, Zhengqin; Xing, Huasong; Fang, Shun; Wu, Shiqian; Xie, Shoulie

doi:10.1109/iccvw54120.2021.00024

Cited by 4 publications

(3 citation statements)

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“…To confirm the efficiency and accuracy of R_GDE, diverse data matrices are utilized in testing to estimate the rank, and the method is compared with two SOTA rank estimate n 2 3000 1000 α 0.1 0.4 0.1 0.4 κ 1 15 30 1 15 30 1 15 30 1 15 30 GDE 98 65 0 100 37 0 99 58 0 100 29 0 RANK 100 95 87 79 78 77 98 94 87 53 52 46 R_GDE 100 100 100 100 100 100 100 100 100 100 100 97 Table 1: The accuracy of estimated rank by using R_GDE (ours), GDE (Xu et al 2021a), and RANK (Xu et al 2021b) with varying size of matrix (n 1 = 3000), varying outlier sparsity α and varying condition number κ. approaches: GDE (Xu et al 2021a) and RANK (Xu et al 2021b). The tests of synthetic matrices with varying settings are based on 100 Monte Carlo runs, Table 1 illustrates the results of these tests.…”

Section: Comparison Of Various Rank Estimation Methodsmentioning

confidence: 99%

“…The target rank is a critical parameter during LRMR, it is, however, unknown in most practical applications. While two different rank estimation methods were proposed in GDE (Xu et al 2021a) and RANK (Xu et al 2021b), they are not suitable for an ill-conditional matrix characterized by a large condition number κ, as illustrated in Fig. 1.…”

Section: Rank Estimationmentioning

confidence: 99%

“…Synthetic Datasets For synthetic datasets, we compare LERE against SOTA RPCA-based methods categorized into two groups: The first category is based on the estimated rank, including ARE-RPCA (Xu et al 2021a) and ADW-RPCA (Xu et al 2021b). The second group is grounded on prior rank, featuring AccAltProj (Cai, Cai, and Wei 2019), ScaledGD (Tong, Ma, and Chi 2021), RPCA_HQF (Wang et al 2023), and LRPCA (Cai, Liu, and Yin 2021).…”

Section: Comparison Of Various Rpcamentioning

confidence: 99%

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

Xu,

Zhang,

et al. 2024

AAAI

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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.

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