An Improvement of Two-dimensional Robust Principal Component Analysis Based on ADMM Solution

Robust principal component analysis (PCA) is an important data dimensionality reduction algorithm. The traditional method to measure recovery error by F-norm is highly sensitive to noise. This paper proposed a modified two-dimension Robust PCA (M2DRPCA). M2DRPCA uses Lp,q-norm to measure the recovery error and introduces the joint regularization term of L1,1-norm and F-norm to constrain the low-dimensional representation matrix of the sample, which enhances the robustness to noise and effectively avoids overfitting. An algorithm for solving M2DRPCA is presented. considering that the subproblem can be divided into some blocks, the alternate direction multiplier method (ADMM) is proposed to solve M2DRPCA. The result of numerical experiments shows that M2DRPCA has smaller recovery error than other models, which proves the effectiveness of the work.