Research On Algorithm And Application Of Functional Data Analysis

The rapid development of the Internet has provided us with great convenience in collecting data.The types of data in different fields are diverse and the degree of complexity is different.Through observation and analysis,we can always find that many data have certain rules,Most of them have the characteristics of functions.When analyzing these data,we can use functional data analysis as an important method.The basic idea of functional data analysis is to treat data with functional properties as a whole for analysis and corresponding processing.Among them,"functional" refers to the internal structure of the data,not the external manifestation.The application scope is relatively wide,such as finance,medicine,meteorology,industry and so on.Functional linear regression model is a very important tool for functional data analysis.We can study the relationship between predictive variables and response variables through functional linear regression models.China's economy is booming.However,the quality of the air we breathe every day is not optimistic.Although there is very little PM2.5 in the air,its harm cannot be ignored.PM2.5 can stay in the air for a long time,and can spread to a distance,which is one of the causes of foggy weather.When PM2.5 enters the human body,it can cause airway obstruction or inflammation,which seriously affects people's respiratory function and causes some respiratory diseases.For pregnant women,it affects not only herself,but also the normal development of the fetus.Therefore,it is of great significance to study the cause of PM2.5.This article will use the method of functional data analysis to analyze the relationship between air pressure,temperature,and PM2.5.This article compiled the daily pressure,temperature,and PM2.5 data of 49 cities in China with severe PM2.5 pollution in 2017.These data are all functional data.We first fitted the air pressure,temperature,and PM2.5 of these 49 cities,so that these discrete data obtained from sampling were converted into functional data with acertain regularity.Then a univariate functional linear regression model was used to study the effect of air pressure on PM2.5 and the effect of temperature on PM2.5,which are the effects of a single factor on PM2.5.Finally,using air pressure and temperature as two predictive variables and PM2.5 as a response variable,a multivariate functional linear regression model was used to study the effects of two factors,namely,air pressure and temperature on PM2.5.We focus on the effects of pressure and temperature on PM2.5 when the number of basis functions is different.