Research On Sparse And Robust Low-Rank Matrix Analysis Methods

Due to the rapid development of information technology,massive data are being generated throughout scientific reasearch,engineering and social life every moment,underlying which there is much valuable but hardly observed information.Different from the traditional assumption that the observations are independent and identically distributed,such data are often correlated.Low-rank matrix analysis provides a powerful tool for modeling and processing such data,and thus has attrcated much attention in real applications,and become one of the most important methods for data analysis.Existing low-rank matrix analysis methods,however,still have limitations,such as lack of interpretability and computational robustness.To deal with these issues,we propose several lowrank matrix analysis methods by using block coordinate descent technique,Bayesian methodology,noise modeling principle and self-paced learning strategy.The main contributions can be summarized as follows*:?1?We propose new sparse principal component analysis?PCA?and nonnegative sparse PCA algorithms based on block coordinate descent technique.In this work,we decompose the original sparse PCA problem,with relatively large scale,into a series of small subproblms,and then alternatively solve these subproblems.Since each of the subproblems has a closedform solution,the proposed algorithms are not only simple and efficient,but also with high accuracy.Experiments show that the performance of the proposed methods are better than that of the existing methods.?2?We propose a new L₁-norm low-rank matrix factorization method based on Bayesian methodology and variational inference technique.In this work,we first build probabilistic generative models by utilizing the probabilistic interpretation for L₁-norm.Then we estimate the posterior of the involved parameters via variational inference,within the Bayesian framework.Due the adaptive regularization led by Bayesian methodology,the new method can significantly alleviate the overfitting problems of the existing methods.Besides,because of the efficiency of the adopted variational inference technique,the complexity of the proposed method is not too high.Experiments show that the new method has better computational robustness and accuracy,especially for estimating missing values in the observed matrix,compared with the existing methods.?3?We propose a new robust PCA method based on noise modeling principle,within the Bayesian framework.In this work,instead of single-type noise assumption,we model the complex noise in real problems as a mixture of Gaussians,and construct a new probabilistic generative model for robust PCA.Then we use the variational inference technique to solve the proposed model.Experiments show that,the new method can better fit various types of noise with accurate estimation for the noise parameters,and thus can faithfully recover the low-rank matrix underlying the observed data.Besides,the proposed method can extract noise with physical meanings in several real data,such as face images and surveillance videos.This suggests potential applications of the proposed method in image processing and computer vision problems.?4?We propose a new computation framework for low-rank matrix factorization based on selfpaced learning strategy.In this work,inspired by the learning process of humans,we propose a new low-rank matrix factorization framework by gradually including data from easy to complex,and then apply it to L2-norm and L₁-norm matrix factorization problems.Experiments show that,the new computation framework significantly improves the computational robustness of the existing low-rank matrix factorization methods,and is very effective for structure from motion and background subtraction applications.