Improvement And Application Of Factor Analysis Method Based On Spatial Constraint

Spatial data shows explosive growth and it has had an important impact on social development.However,spatial data is usually interrelated,causing a lot of information redundancy and duplication.Factor analysis is a commonly used method of data dimensionality reduction based on multivariate statistics.In GIS,scholars directly use factor analysis,and the application also stays in its own statistical function.However,traditional statistics for studying random variables has shortcomings in analyzing spatial data.When factor analysis is directly applied to the dimensionality reduction processing of multivariate data in geographic units,the results are biased or non-optimal,which is a false explanation was produced for the actual problem.Aiming at regionalized variables,this article adds spatial constraints to factor analysis,and constructs a spatially weighted geographic factor analysis method and a spatially similar geographic factor analysis method,these methods consider the influence of spatial distribution characteristics of geographic elements when reducing data dimensionality.The spatial weighted geographic factor analysis method integrates spatial weighting into the factor analysis method,and improves the correlation coefficient matrix into a weighted correlation coefficient matrix,so that in the process of reducing the dimensionality of multiple regional variables,the importance of the geographical location with a relatively large weight is increased.The spatial similarity geographic factor analysis method measures the similarity of the spatial distribution characteristics of two regionalized variables based on the similarity coefficient matrix,and extracts multiple regionalized variables with similar spatial distribution structures into a few comprehensive spatial distribution structure factors.The inherent spatial distribution structure of the original regionalized variable set is extracted.This article uses these improved methods to reduce the dimensions of 18 influencing factors of carbon emissions across the China(except Tibet,Hong Kong,Macau and Taiwan).Both improved methods extract 5 common factors.Analyzing the amount of information explained by the five common factors to the original variable set,the correlation of the main explanatory variables within the same common factor,and the correlation of the common factors,it is obtained that the two geographic factor analysis methods have achieved the effect of dimensionality reduction.The influencing factors obtained by the spatially weighted geographic factor analysis method are ranked in order of importance: the factor of population size,opening to the outside world and technological development > the factor of economic development,population urbanization and education level > the factor of technology application level > the factor of second industry proportion > the factor of natural gas consumption proportion.And compared with factor analysis,the results of this method are more suitable for the actual problems studied.The spatially similar geographic factor analysis method extracts five spatial distribution structure factors shared by the original variable sets,and the order of information is: the factor of the agglomeration of the east and the west and central anomaly distribution > the factor of the agglomeration of the west and an anomalous distribution in the east > the factor of central agglomeration > the factor of the agglomeration of Shandong and its surroundings > the factor of the agglomeration of Inner Mongolia.The improved methods based on spatial constraints extends the dimensionality reduction principle of the factor analysis method for random variables to the dimensionality reduction of regionalized variables,which has theoretical and practical value for studying the data dimensionality reduction of multiple regionalized variables.Application research shows that the two geographic factor analysis methods have achieved the effect of dimensionality reduction,and have practical significance and feasibility.