• Public space. Hot spots were initially limited to one side of the street, raising the question of how street curtilage (public space in front of private properties) would be treated. Common sense dictated that if a patrol car was across the street, technically outside the hot spot, it should be considered in the hot spot, so the definition was modified to include both sides of the street.

• Intersections. Ambiguities surrounded the definition of an intersection. The term eventually came to include not only the street, but also adjacent sidewalks and buildings. Even when a hot spot did not technically include all four corners of an intersection, it was found that the best viewpoint for seeing around a corner might be on the other side of the street, outside the hot spot. Thus, all four corners of intersections came to be included in hot spots.

• One-block exceptions. Irregular blocks with large open spaces contained some hot spots, making exceptions to the one-block rule.

In practice, hot spots are defined in numerous ways, some with rigid criteria, like those above, and others with a more flexible approach. None is right or wrong. Both approaches have pros and cons, and an informal cost-benefit analysis can determine the ideal criteria in individual locations. The sharply defined criteria may omit many commonsense exceptions (but allow greater comparability in space and time); softer rules permit easy adaptation to local variation (but make comparisons difficult).

Hot spot mapping

A detailed presentation of hot spot mapping methods is beyond the scope of this guide. However, an investigation sponsored by the Crime Mapping Research Center at the National Institute of Justice in 1998 can offer some tips. This assessment found that most hot spot analysis methods fall into one of five categories: visual interpretation, choropleth mapping, grid cell analysis, cluster analysis, and spatial autocorrelation (Jefferis, 1999; see also Canter, 1995).

• Visual interpretation. The survey showed that, of the police departments that do computer mapping, 77 percent conducted hot spot analyses. Of these, 86 percent identified hot spots visually, and 25 percent used a program to perform this task (Mamalian and La Vigne et al., 1999). The problems presented by the visual approach include overlapping points, points stacked on top of one another, making it impossible to see how many incidents are represented⁵ (that is, only one appears at any given location). Most serious, perhaps, is that readers' interpretations of point data vary, resulting in different interpretations of the same patterns.

• Choropleth mapping. Areas are shaded according to their data values, by either rate or frequency. The caveats mentioned in chapter 2 still apply—class interval selection methods will affect the appearance and interpretation of the map (see figures 2.15 and 2.16), as will color choices, shading levels, and size variation among the polygons. The latter elements tend to draw attention to the largest areas, particularly when they have higher data values.

• Grid cell analysis. A grid is superimposed over a map. Points within cells, or within a designated radius from the centers of the cells, are assigned to the cells. The size of cells is variable and affects the outcome of the analysis. Small cells present higher resolution, at the cost of more computer resources. With larger cells, resolution suffers, but computation is easier. What is the advantage of grid cell analysis over a pin map? First, adding points to the grid solves the problem of "stacked" data points, which occurs when multiple incidents occur at the same location or nearby locations. Second, the points are transformed into a smooth surface, generalizing the data. (For related methods, see the appendix: ArcView Spatial Analyst Extension, Idrisi, Vertical Mapper, the U.S. Department of Justice Criminal Division Hot Spot Slider.) Several examples of grid cell analysis have been illustrated in figures 4.11, 4.12, and 4.13. Another map of this type is shown in figure 4.17, which depicts hot spots in the United Kingdom city of Nottingham and police perceptions of hot spots. This map was produced using the custom program known as SPAM (Spatial Pattern Analysis Machine), which links to MapInfo for the finished map (see appendix). Variations of surface mapping include three-dimensional renditions, as noted in chapter 1. One key to readers' perception of three-dimensional maps is the degree of vertical exaggeration in the map. In the examples shown in figures 4.18 and 4.19 of Salinas, California, quite different types of data (firearm crimes and gangs) are shown in three dimensions.
  
  
  

• Cluster analysis. Cluster analysis methods depend on the proximity of incident points. Typically, an arbitrary starting point ("seed") is established. This seed point could be the center of the map. The program then finds the data point statistically farthest from there and makes that point the second seed, thus dividing the data points into two groups. Then distances from each seed to other points are repeatedly calculated, and clusters based on new seeds are developed so that the sums of within-cluster distances are minimized. (For related methods, see the appendix: STAC, SaTScan, SpaceStat, and Geographic Analysis Machine (GAM.) Figure 4.20 illustrates hot spots derived from the STAC method, which performs the functions of radial search and identification of events concentrated in a given area (Levine, 1996).
  

• Spatial autocorrelation. This concept relies on the idea that events that happen in different locations may be related. In a crime hot spot, for example, underlying social and environmental processes generate crimes in a small area. Multiple events, such as the presence of drug markets, may have similar causes. This means that statistical measures of this condition, known as autocorrelation, can serve as hot spot indicators (Roncek and Montgomery, 1995).