Clustering and Networks
Local spatial association statistics such as local Moran’s Ii and Getis-Ord’s Gi* have heavily been exploited for exploratory spatial data analysis (ESDA). Bivariate versions of local spatial association statistics such as local cross-Moran and local Lee’s Li* have also shown their possibilities as visual analytical tools for bivariate situations. It however should be noted that the development of visual techniques utilizing global spatial association statistics have been limited to a large extent. This is mainly due to the fact that global statistics in nature are targeted for capturing an overall trend of spatial patterns, allowing little room for data exploration. However, this study contends that more visual analytics utilizing global statistics should be developed to meet various needs for ESDA. Another issue is a lack of efforts to link global and local statistics for ESDA in a visual setting: they should be made directly comparable to each other and simultaneously visible for exploratory analytics (e.g., Moran scatterplots).
To date, most popular ESDA techniques utilizing global spatial association statistics might be correlogram and cross-correlogram. The former is related to a graph on which there are different spatial lags on the x-axis and the corresponding Moran’s or Geary’s statistics on the y-axis. It hints the nature of spatial structure and the extent to which a spatial autocorrelation process operates. The latter is a simple extension of the former, providing a graph on which there are different spatial lags on the x-axis and the corresponding cross-Moran statistics on the y-axis to show different levels of spatial cross-correlation between two variables at different spatial scales.
This research proposes a new set of visual techniques called spatial clustogram and co-clustogram which are comparable respectively to correlogram and cross-correlogram. The main difference is that the former are more concerned with the nature and extent of spatial clusters rather than those of spatial association between a reference area and its neighbors. This entails significant differences in some specifics: (i) Si* for clustogram and Li* for co-clustogram are used; (ii), related to (i), spatial proximity matrices having non-zero values on their main diagonals are used; (iii) neighbors at different scales are defined in an additive way rather than in an exclusive way such that neighbors at a particular spatial scale encompass all the neighbors in the previous, smaller, spatial scales. For summary, spatial clustogram and co-clustogram are expected to allow researcher to explore spatial autocorrelation structure and gauge an average size of possible spatial clusters respectively for univariate and bivariate situations. This technique can be extended to embrace other situations dealing with different temporal points of one variable or a pair of variables and a set of different variables.
Particular strategies should be employed for more effective and efficient visual analytics for spatial clustogram and co-clustogram. First, each graph is drawn with a series of box or violin plots for different spatial scales with all the data points representing local statistics. When you select a data point (or multiple data points) on a plot for a particular spatial scale, selections of the corresponding data points at other spatial scales are made with a line (or lines) of linking all of the points. Second, a combination of brushing and linking facilitates a simultaneous examination of the relative position and geographic context of data points by allowing researchers to brush data points of interest on plots and then to make them displayed on the linked maps (or vice versa). An add-on type application equipped with all the features is developed.
Seoul National University
I received my bacherlor's and master's degrees from Seoul National University in South Korea and my Ph.D. degree from the Ohio State University in the US. I have been a professor in Seoul National University since 2003 and am currently a visiting scholar in the University of Texas at Dallas.
University of Texas at Dallas
I received my bachelor's and master's degrees from Seoul National University in South Korea. I am currently a Ph.D. student in Geospatial Information Sciences program in the University of Texas at Dallas.
U.S. Geological Survey
Lawrence Stanislawski is a cartographic research scientist for the Center of Excellence for Geospatial Information Science within the National Geospatial Program of the United States Geological Survey. He studied surveying and forest resource conservation at the Univesity of Florida, and he currently lives in Rolla Missouri. His research interests involve generalization, multiscale representation, geospatial data accuracy, and high performance computing.
Monday, July 3
1:50 PM – 2:10 PM
Monday, July 3
2:10 PM – 2:30 PM
Tuesday, July 4
1:30 PM – 1:50 PM
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