Results
Fuzzy Mode
Illustrated in Figure 4 is the result of the fuzzy mode frequency analysis. It can be observed that the hotspots for weapon violation mainly concentrated in the central-west, southwest, and far south end of Chicago. The communities associated with the clustering of hot spots identified are summarized in the Table 4.

Table 4. Summary of hot spot locations from Fuzzy Mode analysis.
Fig.4 Fuzzy Mode frequency analysis
NNH and RNNH
Comparing Figure 5 to Figure 6, the overall distribution pattern of crime clustering appears to be reasonably consistent between the output for NNH and RNNH, with an exception for the region towards the far southwest side, where only RNNH produced clusters. This observation with the clusters found with the RNNH result, however, appears to coincide with the results from single and dual kernel density estimations.

Fig. 5 NNH Clustering Analysis

Fig. 6 RNNH Clustering Analysis with three order classes
Kernel Density
The single and dual kernel density maps are presented in Figure 7. Dual kernel density takes population into consideration, where single kernel density does not. Therefore, the dual kernel density is often compared with RNNH since the two is expected to be similar in terms of the locations of clustering or places with high likelihood of crime occurrence.
Rogers Park and West Ridge appear to be the two communities with the highest likelihood that weapon violations would occur from both the single and the dual kernel density outputs. Based on the output for dual kernel density, communities with higher than normal likelihood of weapon offences are summarized in Table 5. As expected, Chicago O’Hare International Airport, located on the far northwest end of the city, exhibited the lowest likelihood value in both analyses.
Table 5. List of communities with high likelihood of weapon violations based on the dual kernel density estimation.
Overall, the results from the three types of crime analyses are generally consistent in terms of identifying the locations with high crime rates. The only location that the Fuzzy Mode analysis failed to capture is around the northeast corner of the city (Rogers Park). Land features appear to play an important role in determining the locations of high crime occurrence. In this case, it can be observed that the areas with the highest likelihood of weapon violations generally fall around major road networks such as Highway 57, 90 and 94. On the other hand, major water bodies such as the Chicago Sanitary and Ship Canal act as a “barrier” that separates the city into two parts, which in turn significantly alters the spatial patterns of crime distribution. It is found that weapon violation incidents tend to be significantly more dispersed around water bodies, even with the presence of a major highway.

Fig. 7 Single and Dual Kernel Density Estimations