Functional Data Classification Method And Its Application

The theoretical research of functional data analysis has been well developed.At present,the application research of functional data analysis has also received more and more attention from scholars.The functional data classification problem is an extremely important part in the application of functional data,and the classification problem is mainly divided into supervised classification and unsupervised classification.This dissertation mainly studies PM2.5 and temperature based on functional data analysis,using supervised classification and unsupervised classification methods,then obtained corresponding results respectively.The main results are as follows:(1)PM2.5 classification based on functional non-parametric k-nearest neighbor methodBased on the k-nearest neighbor classification method of functional data,the average PM2.5 concentration of the day is classified by the temperature of 24 hours a day.In this paper,a functional data analysis method is used to select 24 hours a day of temperature data as an independent curve sample,and on this basis,a functional k-nearest neighbor classification model is established to classify and judge the 24-hour average PM2.5 concentration of the day.The quadratic kernel function,exponential kernel function,and triangle kernel function are selected respectively to establish the k-nearest neighbor model,and the results are analyzed.By comparison,it is found that the triangle kernel function is used to accurately classify PM2.5 highest and most robust.Then,based on the triangle kernel function,we compare the actual results of the principal-component semimetrics and the second derivative semi-metrics.The results prove that the second-order derivative semi-metrics are better on this data set.The NW kernel method is compared with the k-nearest neighbor method.The results show that the k-nearest neighbor method can effectively improve the classification accuracy.(2)Temperature research based on functional nonparametric clustering methodFirst,based on the principal component analysis of functional data,conduct a preliminary study on the sample data to analyze the trend of the data itself.Then,based on the functional nonparametric clustering method,cluster analysis is performed on the data of 33 stations in Anhui Province,and a nonparametric clustering model is established to cluster the station temperature data and analyze its second derivative properties.The results show that the functional nonparametric clustering method can cluster the data set well.