Research And Application Of Functional Principal Component Analysis

In recent years,with the progress of science and technology and the pop-ularity of big data,multivariate statistical analysis has been more and more applied.Functional principal component analysis(FPCA)uses functional data analysis method to transform the discrete observation sample data,and then extracts and analyzes the principal components of the function from the transformed functional data.It is an effective and cost-effective dimension reduction method.Multi index sample data set is very common in the analysis of specific ex-amples.In this type of problem,there may be a certain degree of correlation between variables,which leads to a lot of duplication of effective information reflected by sample data,which will bring a lot of invalid work,The more complex the distribution of sample data in high-dimensional space,the more difficult it will be to analyze practical problems.Therefore,in the analysis of actual cases,we hope to use fewer comprehensive variables to represent the original sample data information,and require that these comprehensive variables are not related to each other.In this paper,the precipitation data of 34 cities are functionalized by the basis function smoothing method,and then uses functional principal component analysis method to extract the func-tional principal component.The result diagram is drawn by using R software.Finally,the conclusion is drawn based on the analysis of the actual situation.