Classification Model Of Riemannian Manifold Function Data

With the development of modern technology,data acquisition technology and data storage capacity have been significantly improved,which makes it easier to obtain func-tional data in many scientific fields.Functional data is closely related to our life and is also very common in life,such as someone's ECG,latitude and longitude data of a flight,Doppler contrast-enhanced ultrasound data,etc.from this,we can see the impor-tance and necessity of studying functional data.Since Ramsay put forward the concept of functional data,functional data analysis has always been a research hotspot.With the deepening of research,nonlinear structural data continue to emerge,such as brain computer interface data,bird migration trajectory and so on.Because Riemannian man-ifolds are usually not vector space,many traditional theories and methods of functional data analysis are no longer applicable,so it is very necessary to establish the theories and methods of Riemannian manifold functional data.In order to solve this problem,Lin and Yao constructed an intrinsic Riemannian function data analysis framework,which provides a theoretical basis for the asymptotic analysis of Riemannian manifold function data.Functional data classification is an application direction of functional data analysis.The relevant theories are perfect and there are many models,but there is little research on functional data classification of Riemannian manifold at present.Based on the anal-ysis framework of intrinsic Riemannian function data,this paper proposes the Logistic regression model of Riemannian manifold function data(iRFLM)and the support vec-tor machine of Riemannian manifold function data(iRFSVM).At the same time,the numerical simulation is carried out on the SPD manifold,and iRFLM,iRFLSVM with linear kernel and iRFKSVM with Gaussian kernel are applied to the classification of aircraft flight trajectory.The simulation results show that iRFLM and iRFLSVM per-form better in linear data structure,and iRFKSVM performs better in nonlinear data structure.The model has certain application value.