Research On Data Representation Algorithm Based On Low Rank Matrix Recovery

The Low Rank Matrix Recovery algorithm is a kind of dimensionality reduction algorithm which attracted widely attention in recent years.The algorithm divides the sample into low-rank matrix and sparse matrix.The low-rank matrix is the approximates of the original data,which can effectively remove the noise and the outliers in the sample.While the sparse matrix contains noise and outliers.Low rank matrix recovery theory includes Robust Principal Component Analysis(RPCA),Matrix Complements(MC),and Low Rank Representations(LRR).Robust Principal Component Analysis is mainly applied to image reconstruction and denoising,and Low Rank Representation algorithm has obvious advantages in data segmentation and clustering.In this paper,we mainly study and analyze the two algorithms and their related extended algorithms,and then improve their shortcomings.Firstly,the research status of Low Rank Matrix Recovery theory is introduced.And we make a detailed description of Robust Principal Component Analysis(RPCA)and Low Rank Representation(LRR),analyze the applications fields and advantages and disadvantages.The main work of this paper includes:After deeply studying Robust Generalized Low Rank Approximations of Matrices(RGLRAM)algorithm,this paper proposed a new video restoration algorithm based on it.The algorithm can deal with a group of images rather than just a single image,and robust to sparse noise.In this paper,RGLRAM is extended to the field of video processing.The video is grouped according to the coordinate position,the reconstruction result of each group is carried out respectively.Finally,the reconstructed video is reconstructed according to the position of coordinates which has been marked.The algorithm makes full use of the information among the frames to remove noises,meanwhile,the uniqueness of each frames can be preserved very well.The experimental results simulated by MATLAB are analyzed in detail.Finally,after fully studying the Low Rank Representation and its improved algorithms,we propose a new improved algorithm of LRR----Robust Discriminant Low Rank Representation(RDLRR).Low rank representation is often used for data clustering and segmentation,and the key to the completion of this work is to find the similarity matrix.The existing methods mainly to improve their robustness,while ignoring the discriminant.Based on the classical low rank representation,our algorithm increases a discriminant terms which considers the within-class distance and between-class distance.Thus,RDLRR can not only preserve the robustness of classical method,but also increase the discrimination of similarity matrix.Finally,we use Ncut or Kmeans method to cluster the similarity matrix and get the final results.In this paper,we do experiments on several data sets.Compared with other methods,the accuracy was significantly improved.And the experiment proves that our method is insensitive to the parameter values.