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A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time…
Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer…
City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature…
Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer…
Moran's index is a basic measure of spatial autocorrelation, which has been applied to varied fields of both natural and social sciences. A good measure should have clear boundary values or critical value. However, for Moran's index, both…
Spatial autocorrelation analysis is the basis for spatial autoregressive modeling. However, the relationships between spatial correlation coefficients and spatial regression models are not yet well clarified. The paper is devoted to explore…
Spatial autocorrelation plays an important role in geographical analysis, however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore,…
Spatial interaction and spatial autocorrelation are two different fields of geo-spatial analysis, revealing the internal relationship between the two fields will help to develop the theory and method of geographical analysis. This paper is…
Moran's index and Getis-Ord,s indices are important statistical measures of spatial autocorrelation analysis. Each of them has its own function and scope of application. However, the association of Moran index with Getis-Ord index is not…
In statistics, the Durbin-Watson test is always employed to detect the presence of serial correlation of residuals from a least squares regression analysis. However, the Durbin-Watson statistic is only suitable for ordered time or spatial…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…
Moran's I statistic, a popular measure of spatial autocorrelation, is revisited. The exact range of Moran's I is given as a function of spatial weights matrix. We demonstrate that some spatial weights matrices lead the absolute value of…
Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data…
Physical or geographic location proves to be an important feature in many data science models, because many diverse natural and social phenomenon have a spatial component. Spatial autocorrelation measures the extent to which locally…
Comparing spatial data sets is a ubiquitous task in data analysis, however the presence of spatial autocorrelation means that standard estimates of variance will be wrong and tend to over-estimate the statistical significance of…
Compositional observations arise when measurements are recorded as parts of a whole, so that only relative information is meaningful and the natural sample space is the simplex equipped with Aitchison geometry. Despite extensive development…
The Local Moran's I statistic is a valuable tool for identifying localized patterns of spatial autocorrelation. Understanding these patterns is crucial in spatial analysis, but interpreting the statistic can be difficult. To simplify this…
Networks where each node has one or more associated numerical values are common in applications. This work studies how summary statistics used for the analysis of spatial data can be applied to non-spatial networks for the purposes of…
This study develops a spatially varying coefficient model by extending the random effects eigenvector spatial filtering model. The developed model has the following properties: its coefficients are interpretable in terms of the Moran…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…