A Research On Quaternion Parallel Feature Extraction Of Multivariate Functional Data

Functional data analysis has been developed rapidly in recent years.It has been widely used in various fields such as meteorology,finance,medical treatment and so on.However,as a new branch of science,there are many problems to be further studied.For example,the traditional functional data analysis theory mainly aims at the unary functional data,and the research of multivariate functional data is not enough.In the treatment of multivariate functional data,it is simply string together the multiple functions into a long function.It ignores the correlation between multivariate functions.Consequently,there is a lack of efficient parallel processing method.In this paper,the quaternion signal processing method is apply into the field of functional data analysis.Based on the idea of "functional and integral representation",we propose a kind of quaternions embedding representation model of multivariate functional data using the quaternions as a mathematical tool.The multivariate functional data is represented as a multi vector function of the quaternion space,so that we can use the existing quaternion signal processing algorithm to analyze the multivariate functional data parallelly from the perspective of quaternion.In this paper,we mainly study the parallel feature extraction of multivariate function data based on the quaternion principal component analysis and the pattern classification based on parallel features.ECG is a process that reflects the electrical activity of the heart.It can be used to analyze and identify various arrhythmias,but also to reflect the extent of myocardial damage and the development process,as well as the functional structure of atrial and ventricular.Therefore,ECG has an important reference value in the study of the basic function and pathology of the heart.In this paper,the proposed algorithm is used to classify and evaluate the PTB diagnostic multichannel ECG data set of the PhysioBank database.Firstly,the original ECG data is represented as a functional data after pretreament.Secondly,embed them into the quaternions embedding representation model of the multivariate functional data.Finally,the quaternion principal component analysis is used to extract the multi channel fusion features and do classification based on supportvector machines.By comparing the results of the traditional functional data analysis and the traditional quaternion principal component analysis prove that the quaternion principal component analysis method based on functional data proposed in this paper is better than the traditional methods.