Figure 5‑13 illustrates a number of alternative methods for exploring variations in mapped point-based datasets with associated weights or continuously variable attributes. As in Figure 5‑10 the (Sample 1) dataset consists of location information for 200 radioactivity monitoring stations in Germany, together with the levels of radiation recorded on a single day in 2004. A simple ESDA approach is to map the data and apply symbology to reflect the data values recorded. In Figure 5‑13A and B this is illustrated by the use of variable symbol size and/or color to reflect underlying values. In Figure 5‑13C a more sophisticated analysis has been conducted. In this case a semivariogram scatterplot (see further, Section 6.7.1, Core concepts in Geostatistics) of the dataset was generated (using ArcGIS Geostatistical Analyst) and the set of points on the scatterplot with the highest semivariance values were selected by brushing. Since these points in the scatterplot represent data pairs the linked map highlights the pairings. As can be seen the most extreme semivariance values are all related to just two of the original 200 source points in the lower right of the map. It may be that these latter points are of special interest (have unusually high or low radioactivity measurement) or that the data are incorrect and require adjustment or removal of selected values.

Figure 5‑13 Exploratory analysis of radioactivity data

A. Variable point size |
B. Variable color |
C. Semivariogram pairs |
D. Voronoi analysis, cluster |

The last of the four images shown, Figure 5‑13D, shows a rather different form of ESDA. Voronoi polygons (see Section 4.2.14, Tessellations and triangulations) have been generated for the MBR of the entire point set and the radioactivity data mapped based on cell adjacencies. A set of 5 classes has been defined and cells that fall into a different class interval from all of their immediate neighbors are colored gray, otherwise they are colored by class interval. Note that these outliers are determined spatially, and will not in general correspond to extreme data values — they are local spatial outliers. Other Voronoi region statistics available as an alternative to this cluster approach include: mapping actual radioactivity values (described as “simple” mapping); using a local neighborhood mean or median for all cells; allocation based on a local neighborhood entropy statistic (see Table 1‑3); and spread-based statistics, such as standard deviation and range-based mapping.

Table 5‑3 Voronoi-based ESDA

Local Smoothing |
Mean, Mode, Median |

Local Variation |
Standard deviation Inter-quartile range Entropy |

Local Outliers |
Cluster |

Local Influence |
Simple |

A summary of the interpretation of each of these choices is provided in Table 5‑3 (these may be compared with some of the grid analysis methods described in Section 4.6, Grid Operations and Map Algebra).