Principal Component Analysis Of Spatio-temporal Data Based On Tensor And Its Application In Economic Rating

With the advent of big data era,high-dimensional,dynamic,and multi-element spatio-temporal data sets show a trend of massive expansion,and the demand for principal component analysis of spatio-temporal data has gradually revealed.Tensors can reflect the interaction between two or more dimensions,and are the ideal structure for the expression,calculation and analysis of spatio-temporal data.Therefore,the principal component analysis method based on tensor data has been proposed and developed,and has been applied in the fields of chemistry,medicine and geography.In this paper,this method is first applied to the economic data.The time series data of 13 economic indicators of 31 provinces in China in the past 21 years are expressed in the form of spatiotemporal tensors,fully retaining the spatio-temporal structure in the data.Then,using the tensor-based principal component analysis method(principal tensor analysis on k-modes)to study the main feature of the data,four principal components were extracted,and the cumulative variance contribution rate was 75.82%.Finally,based on the score coefficients of these principal components in various dimensions,a comprehensive evaluation index of each province's economy is constructed and the scores of each province are calculated,thus giving the economic ranking of each province.The research in this paper demonstrates a different economic rating method,which can more comprehensively integrate spatio-temporal information and improve the comprehensiveness of the rating.I hope this rating method can bring better reference value to the national government.