Fuzzy Sparse Deviation Regularized Robust Principal Component Analysis

Robust principal component analysis (RPCA) is a technique that aims to make principal component analysis (PCA) robust to noise samples. The current modeling approaches of RPCA were proposed by analyzing the prior distribution of the reconstruction error terms. However, these methods ignore the influence of samples with large reconstruction errors, as well as the valid information of these samples in principal component space, which will degrade the ability of PCA to extract the principal component of data. In order to solve this problem, Fuzzy sparse deviation regularized robust principal component Analysis (FSD-PCA) is proposed in this paper. First, FSD-PCA learns the principal components by minimizing the square of $\ell _{2}$ -norm-based reconstruction error. Then, FSD-PCA introduces sparse deviation on reconstruction error term to relax the samples with large bias, thus FSD-PCA can process noise and principal components of samples separately as well as improve the ability of FSD-PCA for retaining the principal component information. Finally, FSD-PCA estimates the prior probability of each sample by fuzzy weighting based on the relaxed reconstruction error, which can improve the robustness of the model. The experimental results indicate that the proposed model performs excellent robustness against different types of noise than the state-of-art algorithms, and the sparse deviation term enables FSD-PCA to process noise information and principal component information separately, so FSD-PCA can filter the noise information of an image and restore the corrupted image.