Robust Principal Component Analysis With Incomplete Data

Robust Principal Component Analysis(RPCA),Partial Sum Minimization of Singular Values(PSSV)and Tensor Robust Principal Component Analysis(TRPCA)are three classic effective algorithms which are used in machine learning,pattern recognition areas etc widely,for image denoising and video recovery.RPCA and PSSV can recover potential low-rank structures from second-order data matrices corrupted by sparse noise,and TRPCA can recover potential low-rank structures from high-order data matrices(greater than or equal to third-order)that are corrupted by sparse noise.But when the data is incomplete or some data is completely damaged,the performance of RPCA,PSSV and TRPCA algorithms will be reduced.In order to solve this problem,in this paper,we propose corresponding improved models by In-depth analysis of RPCA,PSSV and TRPCA,and prove their effectiveness in some video sequence and face databases.The main research contents of this paper are as follows:(1)Aiming at the problem that the performance of RPCA algorithm and PSSV algorithm will be seriously degraded when the data is severely damaged,we adds the variance regularization to the low-rank part in this paper,consider the local structure information in the single feature dimension fully,and propose the Robust Rrincipal Component Analysis with Variance Regularization and Partial Sum Minimization of Singular Values with Variance Regularization,namely RPCAR and PSSVR.When the data is incomplete or partially damaged,the regularization term can ensure that the missing part of the low-rank structure is restored by the local structural information,thereby it can improve the robustness of the algorithm to outliers and missing values.From the simulation results of the background extraction and moving target detection of the incomplete video sequence dataset,the image denoising and clustering of the face database illustrate the effectiveness of the RPCAR algorithm and the PSSV algorithm.(2)Aiming at the problem that the TRPCA algorithm does not consider the local structural information of the data,we proposes a Tensor Robust Principal Component Analysis with Variance Regularization in this paper,namely TRPCAR.The algorithm adds variance regularization to the tensor low-rank structure.When part of the data on an order is severely broken,the variance regularization term guarantees the learning of local information,so it can recover the complete low rank structure.TRPCAR has better robustness than the TRPCA algorithm.From the simulation results of the background extraction and moving target detection of the incomplete video sequence dataset,the image denoising and clustering of the face database show that the TRPCAR algorithm has better performance.