Square Root Principal Component Pursuit: Tuning-Free Noisy Robust Matrix Recovery

Principal Component Pursuit for Pattern Identification in Environmental Mixtures

“…We incorporated two PCP extensions that suit features of environmental mixtures data. First, Zhang et al [20] recently proposed √ P CP with a noise-independent universal choice of regularization parameters. Previous formulations of PCP required knowledge of the true noise level to determine the appropriate parameters [22][23][24].…”

“…where X denotes the original data matrix. The two parameters, λ and µ, are not tuned by the researcher; instead, they are each set using single universal values, λ = 1/ √ n from Candès et al [19], and µ = p/2 from Zhang et al [20] which have been shown theoretically to yield near-optimal estimation performance. The indicator function 1 rank(L)≤r constrains L to be of rank ≤ r; the 1 norm S 1 is the sum of the absolute values of the entries of S and encourages S to be sparse; the final term is the error between the predicted and the observed values, which favors a solution that is close to the original data.…”

“…PCP has several advantages over PCA in the area of pattern detection in environmental mixtures. In a recent PCP extension, square root PCP ( √ P CP ), Zhang et al [20] derived a new formulation with a universal choice of regularization parameter. Thus, the user is not required to choose or tune hyperparameters.…”