Weighted Principal Component Score Clustering Analysis Based On Functional Data And Its Application

With the continuous development of network technology in recent years,the skills of people collect and store data are also increasing,more and more data can obtain.In these data,there is a kind of data whose potential generating process is dynamic and continuous,and it has certain functional characteristics in essence,statisticians call it functional data.However,traditional data analysis methods cannot excavate information of functional data fully,then functional data analysis method was born.Functional data analysis has many advantages,and many classical statistical methods can be extended to the analysis of functional data.This paper combines clustering method with functional data,and discusses a series of clustering methods for functional data.It mainly includes the following three aspects:Firstly,the preprocessing methods of functional data are described.Because the collected functional data are discrete in real life,it is necessary to use corresponding methods to estimate the curve of the data,and then to show the intrinsic characteristics of the data.Therefore,this paper discusses the method of base function expansion for fitting curve,icluding selection of basis function type and introduction of least squares smoothing model with penalty term.The advantages of functional data analysis are also summarized,it is proved by an example that the function data can not only overcome the error caused by noise data,but also reduce the influence caused by data abnormality and data missing.Secondly,the clustering analysis is extended to the functional data,and the clustering method of the functional data is studied.In this paper,a weighted principal component score clustering method for functional data with non-orthogonal basis expansion is proposed,the concrete steps of clustering are introduced in detail.At the same time,the validity of the proposed clustering method is verified by random simulation experiments.The classification results show that the new clustering method can cluster the functional data effectively.Thirdly,the new clustering method is applied to the study of the population of 31 provincial capitals in China and compared with the general hierarchical clustering method.,The results show that the new clustering method can not only effectively classify the population of different cities,but also show the changing characteristics of the results of different types of urban population classification and the differences between each type,moreover,the new method reduces the dimension of the principal component of the function,which reduces the computational complexity.Therefore,the functional weighted principal component score clustering method proposed in this paper is feasible and better than the general hierarchical clustering method.