Method And Application Of Functional Clustering Analysis

Cluster analysis is a branch of multivariate statistical analysis and a very important analytical method in data mining at present.In the traditional clustering analysis,whether the analyzed data is the cross-sectional data,the time series data or the panel data,the object of cluster analysis is usually the discrete data,and the corresponding data processing methods are presented in the form of vectors.With the rapid development of information technology,especially the popularization of sensors and the rapid development of storage technology,data in many fields are characterized by the volume and continuity of the sea,the data contains a lot of dynamic information,this kind of data is often regarded as functional data.For functional data,it is difficult for traditional clustering analysis to measure the dynamic characteristics of data in the process of clustering,so the function clustering analysis is proposed.Compared with the traditional clustering analysis,it sees the data as a whole,and from the point of view of the function,it excavates more dynamic information of the data in the process of clustering.For data with function characteristics,the function clustering analysis method can achieve better clustering effect.Based on the advantages of functional clustering analysis method,more and more scholars begin to use functional clustering analysis method,and carry out in-depth research and expansion.Through combing and studying the existing functional clustering analysis methods and traditional clustering analysis methods,it is found that the main research direction of functional clustering analysis method is based on the study of functional data similarity measurement,and points out the main problems existing in the research of functional clustering analysis method at present.The problem of functional data similarity is measured based on a single angle of numerical distance or curve shape.In order to solve this singularity problem,the author puts forward for the first time a similarity measurement method of numerical distance and curve form which takes into account the function type data,which is based on the similarity measure of extreme point compensation,and compares it with the similarity measurement method of several existing functional data.The visualization shows a clearer distinction between the characteristics of the various methods.In order to meet the actual demand more,the author tries to expand the clustering analysis method of single index function by the cluster analysis method(function entropy method)for the first time.In order to verify the effectiveness of the method,the paper uses the traditional clustering method,the function clustering analysis method based on the numerical distance,the function clustering analysis method based on the curve form,and the functional clustering analysis method proposed by the author to take into account the numerical distance and curve form to cluster the Shanghai 50 sample stocks,By using contour coefficients,the clustering results of each method are compared,and the following conclusions are drawn:whether the single index function clustering analysis method or multi-index function clustering analysis method,the effect of clustering analysis is better than the traditional clustering analysis method,and further,the similarity measure based on extreme point offset compensation proposed by the author It is true that the numerical distance and curve morphology of the simultaneous measure function data are achieved,and the function clustering analysis is carried out by using this similarity measure,and the effect of clustering analysis is also improved!...