Research On Spatial Autocorrelation Simulation Data Generation Method And Its Preliminary Application

The problems including low degree of artificial controllability and complicate components of geospatial data in nature caused the failure in a deep and wide study of spatial statistics and spatial regression analysis those are furtherly performed by the researchers.Even if some studies are reluctantly carried out sometimes,conclusion drawn in the study sounds irreliable and the in-depth analyses of the corresponding geographical mechanism are lack.Especially in the study of spatial autocorrelation,many spatial autocorrelation mechanisms are not clear so that the further study of spatial regression analysis fails to be conducted.In order to overcome these challenges,researchers attemps to improve the degree of artificial controlliability of spatial data through generating simulation data in the presence of spatial autocorrelation in the experiment.Through controlling spatial distribution and data structure of artificially spatial data,researchers try to deepen the understanding of analysis results and methods of geospatial data.Unfortunately,up to present,there is little literature on the generation of simulation data with spatial autocorrelation and the reason is that there is not a practical theory for data generation in the presence of spatial autocorrelation.In this work,the methodology of theoretical analysis is applied to study the generation of data with spatial autocorrelation and the application case of the simulation data is utilized to verify the proposed approach is reliable.The research paradigm of asking questions,theoretical analysis and case verification is adopted.Firstly,the theory of spatial autocorrelation simulation data generation is analyzed.In other words,the eigenvalue and eigenvector of spatial weight matrix are analyzed based on matrix algebra theory.The geographical meanings of the eigenvector and eigenvalue are pointed out.On this basis,the theory of spatial eigen-patterns is firstly put forward and developed,and then the representation of global Moran's I using spatial eigen-pattern is presented,next the generation method of spatial autocorrelation's simulation data is proposed and spatial autocorrelation simulation data is produced,and the spatial autocorrelation simulation data is appield to case analysis in the end.The main research topics and conclusions are as follows:(1)The theory of space eigen-pattern is put forward.After analyzing the types and characteristics of spatial weight matrix,based on the matrix algebra theory,the analysis of eigenvalue and eigenvectors based on spatial symmetrical weight matrix is carried out.Based on the orthogonality of eigenvector with each other,the arbitrary spatial patterns are thoughted of to be decomposed into linear algebra sums of all the spatial eigenvectors.In the actual case of 54 research units in Jiangsu Province,typically spatial eigen-patterns with positive and negative spatial autocorrelation are shown through mapping visualization.(2)The generation method of simulation data with spatial autocorrelation is studied.Based on the theory of spatial eigen-patterns,the representation of global Moran's I is presented.From the perspective of spatial eigen-patterns,the characteristics of Moran's I is analyzed.The generation principle and simulation algorithm of simulation data with spatial autocorrelation are proposed.In generating simulation data in the presence of spatial autocorrelation,simulation data with,not only positive spatial correlation but also negative spatial correlation,are engendered.Using the global Moran's I test tool in Arc GIS,the accuracy of the simulation data is verified and the reliability of the method is proved.In simulating,the influences of different types of spatial weight matrix and different spatial eigen-patterns on the simulation results are also discussed.(3)Preliminary application of the simulation data.The generation method of simulation data with spatial autocorrelation is prelimarily applied in the first-order spatial autoregression model.The spatial autoregression coefficient is analyzed.The relationship between spatial autoregression coefficient and global Moran's I,as well as the possible geographic mechanism and characteristics are debated.The results show that the eigenvalue of the spatial weight matrix represents the spatial eigen-pattern and the eigenvalue is the global Moran's index of the spatial eigen-pattern called as eigen-Moran's index.In general,if original observation value is normal distribution then the distribution of decomposition coefficient is also normality.Oppositely,if the spatial data is characteristic of high spatial autocorrelation,only several spatial eigen-patterns are dominant.By analyzing the eigen-pattern of global Moran's I,the several spatial eigen-patterns are found to be related to the spatial distribution.The identical global Moran's I do not infer that their spatial patterns are identical.Enve if global Moran's I do not change,the spatial autocorrelation distribution can still vary with the spatial eigen-patterns.The proposed generation method is used not only to generate spatial positive correlation simulation data but also to generate spatial negative correlation simulation data.In summary,the theory of spatial eigen-patterns proposed in this study is clear.The generation method of simulation data with spatial autocorrelation is simple and practical and the simulation data is under the high control.The introduction of spatial eigen-pattern and eigen-value can provides a new way to solve the issues of geography.The spatial eigen-pattern and spatial eigen-value will be widely and extensively applied in a promising future in reduction or removal of spatial autocorrelation,fraud statistical data identification,spatially causality inference and so on.