Adaptive Rank Estimate in Robust Principal Component Analysis

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

“…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.…”

“…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.…”

“…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).…”

“…this work, we assume that n 1 < n 2 ), where the target rank of L is r and R Y ∈ R n1×n1 . Subsequently, through unitary transformation matrix U t and shrinkage matrix Σ Y from the work of(Xu et al 2021a), the resultant transformed matrix R Σ Y can be acquired as below:…”