Take Advantage Of Lowrank Matrix Approximation To Optimize The Rank

With the development of big data, the more data has been used extensively. Nomatter the information you left in the medical institution or the trace you shopped onthe internet, or the internet location. The gigantic data are recorded and usedextensively. We need to dig the data and evaluate then conclude how to use them. Wewill witness the change brought by the data analysis but at the same time we will feelhelpless for the increasing data.As per the amazing data, people begin to learn by machine. According to theprocession and research to data, we found that lots of data can study by machine andthe problem how to manage the data，there are thousands of data in realistic can beexpressed in matrix form， with the data problems growth, the space and time of dataanalysis will be more complex, which made the large scare of data unaccustomed,then we come up with a new algorithm because of the influence of nonnegativematrix.The rank is the core of information retrieval，how to judge and list theinformation that users are in most need in the first. Up to now, the rank method ofinformation retrieval includes the following two example：Judge the correlation，based on the internet files and conclude the files and userscorrelation.Determine the degree of importance based on the internet link and compare theimportance of web page.At the moment we cannot satisfied with the single learning method, more rankstudy and rank method have been provided. But we put forward a classificationmethod to the query data with data clustering.In this method, we improve the data clustering gradually especially discussing the optimal value and convergence，in comparison，we found that double figureregular method is really good at data clustering and raise the speed, short the actiontime, it played a really important role in our build sorting clustering model.In my paper, we will discuss mainly how to combine low rank matrix andpopular algorithm and made clustering accuracy and speed raised and optimized therank problem:(1) We proved a faster algorithm to solve low rank second half definite quadraticoptimization problem. We discuss nonconvex quadratic matrix positive semidefiniteoptimization problem, because there are special institution which made local optimalsolution is global optimal, and proved in a series of machine problems.(2) Take advantage of manifold data and previous chapter low-rank structure setup double figure regular nonnegative matrix, we use the previous chapter to prove theresult, prove the optimality of the model, and the convergence of the framework takesinto account the data manifold and geometric characteristics of the manifold,according to the comparison the algorithm of clustering is better.(3)Put the applications of this sex better clustering algorithm to sort model,model the data line, then use double diagram to cluster, regular for the new querydata, identifying its classification, the corresponding sort of this kind of function isapplied to the corresponding documents, then obtain query and sorting result.