Two Class Of Low-rank Matrix Reconstruction Models And The Research Of Its Application

With the rapid development of the Internet,sensors,computing resources and other technologies and hardware,the speed and volume of data are huge,and our society has entered the era of big data.Therefore,it is of great significance to explore the big data effectively,to dig out useful knowledge teams to improve the operation efficiency of things,and to understand the law and essence of the development of things.And these data are often in the form of matrix,so the analysis of data matrix is very meaningful.If we put the row of the matrix corresponding to a sample,so there is similarity between sample and sample,the columns of the matrix as described,the characteristics of the sample is also exist similarities between features.So this correlation can be represented by the rank of the matrix.In the real problem,the data matrix we obtain often has the influence of lack,defilement,noise and so on,so the original data matrix does not satisfy the low rank.A natural idea is to study how to reconstruct a low-rank matrix to replace the original data matrix.This is the problem of low rank matrix reconstruction.In reality,there are two kinds of low rank matrix reconstruction problem is common:a class is a data matrix contains a lot of unknown elements,hope in the matrix of low rank through optimization algorithm under the premise of the supplement,called low rank matrix filling problem;The other is that the original data matrix often contains the influence of noise,hoping to remove the noise and restore the low-rank data matrix,which is called the low rank matrix recovery problem.In this paper,we summarize low rank matrix completion models and low rank matrix recovery models.Low rank matrix completion models have elastic-net regularized nuclear norm minimization model,nuclear norm regularized least squares model,the model based on matrix decomposition,a weighted nuclear matrix norm minimization based nonconvex relaxation model,etc.The low rank matrix recovery models have the principal componen-t analysis model based on gaussian noise and robust principal component analysis model based on sparse noise.On the basis of classical model and algorithm,we consider the prob-lem of matrix reconstruction under the influence of row sparse noise and the corresponding alternating direction multiplier method is derived.The improved algorithm is compared with the traditional algorithm by numeric experience and the accuracy and efficiency of different algorithms are summarized to provide reference for modeling specific problems.In addition,this paper discusses the two types of applications.One is a comprehensive ranking of jokes:Based on the score data of the 100 jokes by 23500 users,the unknown score can be predicted by using the low-rank matrix completion model,and the average score of the joke is ranked as the comprehensive score of the joke.The other one is to extract the moving object in video:the same background can be thinked the low rank matrix,the movement of the object can be treated as noise,so as to take advantage of low rank matrix recovery model for moving object extraction.