Method And Application Research On Association Analysis Of Multivariate Data Based On Maximal Joint Information Coefficient

With the rapid development of information technology,the ability of data acquisition and data storage has greatly enhanced.Large volumes of data have been produced from all trades and professions,while large scale and ultra-large scale data storage systems have emerged.Multivariate data,as a widely used data format,exists almost everywhere.In realistic situations,most systems are multivariate,and any component of a system is decided by the interaction of other components.The information related to the law of the system development distributed in all the variables of the system,which cannot be described by one variable solely.Thus the research on the correlation analysis of multivariate data is indispensable in theory and in practice.Traditionally,correlation analysis is based on the theoretic model lacking of accurate data and solved through some specific algorithms.However,for complex systems,open and half-open systems,it is difficult to establish theoretic model.In the era of big data,some inexplicable mechanism can be described by the correlation law between data.Thus this paper systematically studies methods of multivariate correlation analysis base on real-world cases;the main contribution is elaborated as follows:(1)A core method and a general framework have been established for the multivariate data association analysis.Firstly,related basic concepts are introduced and the general mathematical description and the analysis thought of this problem are demonstrated.In allusion to the lack of traditional correlation analysis,the method to deal with big scale and high dimension data has been introduced.After the exploratory analysis method for multivariate data correlation analysis has been studied,the general processing framework for multivariate data correlation analysis is established.A correlation analysis process can be divided into five steps: data acquisition,data preprocessing,data compressing,general correlation analysis and results evaluating.Details to explain the five steps are also given in the paper.(2)Maximal joint information coefficient and other joint information indexes for multivariate data correlation analysis are proposed.Based on the mutual information theory,the maximal information coefficient for two variables has been extent to multivariate variables.The maximal joint information coefficient and other joint information indexes for multivariate data are proposed,of which the meanings and characteristics are respectively illustrated.Then these indexes have been compared to traditional correlation anysis indexes,which is trun out to show the efficiency of the indexes proposed in this paper.(3)An algorithm is come up for solving the maximal joint information coefficient and other joint information indexes for multivariate data.Discussing the algorithms for solving correlation indexes of multivariate information,a theorem that best divisions for information correlation indexes satisfies recurrence relations,is come up and proved.Thus a dynamic programming algorithm is implemented to get the best divisions.Based on the algorithm,the best solving algorithm and approximating solving algorithm for those multivariate information correlation indexes are given.(4)Case studies are carried out on correlation analysis methods of multivariate data.At last,case studies are carried out base on simulation data to verify the effectiveness of the proposed method for multivariate data correlation analysis.After that,based on the real world data,sleep monitoring signals collected from the wrist watches are used as the example to demonstrate the significance of multivariate data correlation analysis.