Related papers: Demystifying Spatial Dependence: Interactive Visua…

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…

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…

Spatial autocorrelation coefficients such as Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation…

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…

In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as Moran's I, which in our language is a score associated to a…

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,…

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…

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…

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…

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…

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…

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…

Evaluating spatial patterns in data is an integral task across various domains, including geostatistics, astronomy, and spatial tissue biology. The analysis of transcriptomics data in particular relies on methods for detecting…

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data…

Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…

Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these…

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…

Detecting dependence between variables is a crucial issue in statistical science. In this paper, we propose a novel metric called label projection correlation to measure the dependence between numerical and categorical variables. The…

This paper presents an interactive technique to explain visual patterns in network visualizations to analysts who do not understand these visualizations and who are learning to read them. Learning a visualization requires mastering its…

Street-level visual appearances play an important role in studying social systems, such as understanding the built environment, driving routes, and associated social and economic factors. It has not been integrated into a typical…