5.1. Near-Repeat Characteristics of Research Area
The near-repeat matrix illustrates the risk level following a crime incident. In the top-left cell of Table 1
, the value of 2.85 indicates that, once a crime incident occurs, another crime incident may transpire within 100 m during the next seven days, as the risk level increases by up to 175% over the normal level. Within the range of 100 m, all the cells within a 42 day period exhibit a higher risk level. This means that the risk level after a crime incident will be heightened for approximately six weeks. From the table, we can see that the top-left cell value is the largest and that the other cell values gradually decrease. Within 14 days and 300 m, the Knox ratios are significantly higher than 1.5. In summary, the experimental results demonstrate an obvious near-repeat phenomenon for burglaries in N.
According to the latest research, burglaries in Beijing and Wuhan also exhibit a near-repeat phenomenon [32
]. Compared with Wuhan and Beijing, N has a special near-repeat pattern characterized by a 14 day and 300 m range. This may be caused by the different research scale. In this research, we employ burglaries that have occurred throughout the city, instead of simply using a single district.
Previous studies have not distinguished between repeat and near-repeat victimizations, whereas we choose to do so here. This is because few crime incidents are reported with accurate coordinates. Most crime locations are recorded in the form of a house number, after which they are marked on an electronic map. It is therefore difficult to distinguish whether two crime incidents occurred at the same location, and there are only a few crime incidents that have the same coordinates. Thus, we combine repeat and near-repeat victimizations.
5.2. Contribution of Hot Spots in Repeat and Near-Repeat Victimizations
In the Knox method, the risk level after every crime incident will increase sharply. Additionally, every crime incident is considered to have the same weight for ‘raising’ the risk level. Previous studies have shown that different categories of crime incidents provide different contributions to repeat and near-repeat victimizations [32
]. Thus, further analysis is required to examine whether one crime incident located within a hot spot will result in a different increased risk level. Consequently, in this section, the contributions of hot spots for repeat and near-repeat victimizations will be analyzed.
Two experiments are developed on different space-time scales to investigate the relationships among hotspots and repeat and near-repeat victimizations; 100 m and seven days and 200 m and 14 days. First, the hot spots are extracted from the crime incidents. Then, a crime incident is divided into two categories; whether it belongs to one hot spot or another hot spot. Subsequently, the space-time distances from hot spots to other crime incidents will be calculated. After combining the counts with the same distances into a space-time band, the near-repeat matrix starting from the hot spot will be generated. Here, we call this initial matrix hot spot the starting near-repeat matrix to distinguish it from a normal near-repeat matrix. Finally, the contributions of hot spots to repeat and near-repeat victimizations are expressed by the ratio of the initial hot spot starting near-repeat matrix to a normal near-repeat matrix.
The contributions of hot spots to repeat and near-repeat victimizations are also expressed by a matrix called the ‘contribution matrix’ in this paper, which shows the proportion of the risk level increase following hot spots. The proportion of hot spot crime incidents to all crime incidents can be used as a benchmark for matrix analysis. A higher ratio than that obtained by the benchmark indicates a higher level of increase by the hot spots. In other words, hot spots have a strong influence on repeat and near-repeat victimizations. A ratio that is close to the benchmark indicates that the hot spot has minimal impact on the crime risk level. Therefore, there is no difference between hot spot crime incidents and other, normal crime incidents. A smaller ratio than the benchmark indicates a lower level of increase due to the hot spots. Therefore, hot spots reduce the crime risk level. In summary, the contribution matrix can reflect whether there are any differences between hot spot crime incidents and other crime incidents in their influence on crime risk levels.
The calculation is conducted separately on two spatio-temporal scales: 100 m-7 days (Table 2
) and 200 m-14 days (Table 3
). On the 100 m-7 day scale, 1254 crime incidents are recognized as hot spot incidents. On the 200 m-14 day scale, 2693 crime incidents are recognized as hot spot incidents. Therefore, the benchmarks are 29.7% and 63.7%, respectively. The hot spot contribution changes gradually with the space-time distance in the two contribution matrices. In general, the contribution level decreases gradually with increasing spatio-temporal distance. As illustrated in Table 2
, the ratio within the 100 m-7 day band shows that 62.2% of crime incidents occurred after the formation of hot spots. This ratio is far higher than the benchmark value of 29.7%. The contribution of hot spots is also higher than benchmark in other space-time bands (the upper-left part, within the 28 day and 300 m band). The contributions of hot spots in near-repeat phenomena are very large in the near-space-time area, whereas this is lower than the benchmark in other bands (29.7%). In general, the hot spot contributions in repeat and near-repeat victimizations represent a very high proportion within the 100 m-7 day space-time band. They remain relatively high in the range of 300 m and 28 days. The experimental results and overall trend in Table 3
are very similar to those in Table 2
. However, there are also some differences between these two results on the two scales. The ratio that is higher than the benchmark in Table 3
occupies a larger range (the upper-left part within 700 m and 42 days), which may be caused by the change in scale. A larger scale hot spot may lead to a wider range of variability.
As mentioned previously, repeat and near-repeat victimizations are not distinguished in this research. Thus, the proportions of repeats and near-repeats are not distinguished here. According to exiting research, repeats contribute strongly to the formation of crime hot spots [31
]. However, this proportion is not investigated here. Nevertheless, the area within 100 m shows a high proportion being contributed by hot spots in both repeat and near-repeat matrices within 100 m. This result also shows a close relationship between the hot spots and near-repeat victimization.
From Table 2
and Table 3
, it is apparent that the hot spots provide numerous contributions to near-repeat phenomena. In other words, crime incidents in hot spots have a greater ability to ‘raise’ risk levels relative to other crime incidents. As such, it is necessary to determine if a given crime incident belongs to a hot spot in the field of crime prediction. It is also necessary for crime prediction and criminal investigations to investigate how much the risk level is increased by a hot spot. This will be analyzed in the next section.
5.3. Distribution of Crime Incidents Based on Hot Spots
This section will analyze and quantify the crime risk level after the formation of hot spots based on the TENRM method. The experiments are performed on two different scales similar to the ‘hot spot contribution’ analysis. Two different scale matrices are obtained (Table 4
and Table 5
), and two diagrams are given to analyze the undulation of the risk level around the hot spots (Figure 3
and Figure 4
). The results on the two different scales are very similar. In general, a shorter space-time distance results in a higher risk level. This is also similar to the result of the ‘contribution matrix’ analysis.
In the result on the 100 m and seven day scale, the risk level within 200 m and seven days is nearly twice that of the normal level. The risk level near the hot spots will also increase simultaneously. For example, a risk level at day ‘0’ and ‘100–200’ m is 2.16 times higher than normal, which suggests an additional week with high crime risk following the hot spots. The risk level deceases as the distance gradually increases within the range of 400 m. However, the risk increases again in the day ‘0’ and ‘400–900’ meter bands. Thus, when a hot spot forms, another high risk location may exist nearby (400–900 m). This phenomenon suggests that different locales may be characterized by high crime risks simultaneously. Before the occurrence of hot spots, the crime risk levels of several adjacent units did not increase significantly. For example, the risk level of the two bands within ‘200’ m and ‘0–7’ days did not increase significantly, although the bands around them have a relatively high risk level (‘<100’ and ‘−15–21’, ‘100–300’ and ‘0–21’). It appears then that hot spot locations occur abruptly coincident with many crime incidents relative to normal conditions. However, the other bands near these bands also have high risk levels. Therefore, it appears that the hot spots move in space and time. This phenomenon has been discussed by Nakaya [33
]. Moreover, the risk level rises significantly from ‘22’ to ‘42’ following hot spots, suggesting that hot spots will move to neighboring locations (i.e. within 100–300 m) and return to former sites three to five weeks later. As observed from the image view of the TENRM (Figure 2
), the transfer and reduction process of the crime risk level is wave-like in nature. In addition, the risk level within 400–800 m increases synchronous with the hot spot, and it continues for one week after the hot spot forms. Thus, to improve the accuracy of crime prediction, it is important to understand that hot spots may occur abruptly, move to adjacent locales, occur simultaneously, and subsequently return to their original location. These characteristics are all very important for crime researchers and investigators.
In the results for the 200 m and 14 day scale, the effects of the hot spot become weak with increasing space-time distance. This is similar to Table 1
and Table 4
. The risk level seven days after the hot spot is 2.66 times higher than normal. In the period from seven days before and 14 days after a hot spot forms, the cells within a range of 500 m all have a higher risk level than normal. This may be caused by the change in the spatio-temporal scale. On a 200 m and 14 day scale, the range of the hot spots increases and more space-time bands are affected. In the bands following hot spot formation (15–35 days, 100–300 m), the risk level becomes very low, and the risk level at higher ranges (15–35 days, 300–500 m) becomes very high. This is similar to Figure 4
inasmuch as crime hot spots move in space and time. The risk level prior to a hot spot is not significant (−15–21, <100), but the nearby bands (−15–21 day, 100–200 m) occur within certain high-risk areas. Therefore, before hot spots are formed, the nearby area (100–300 m) always presents a high risk instead of the original location (<100 m). Beyond that, areas located from 600 m to 700 m from the hot spots also show a high risk. This pattern is similar to that of the band in the aforementioned case in that the risk level also shows a wavy undulation (Figure 4
). As observed from the experimental results on the 200 m-14 day scale, the patterns before and after hot spots are roughly similar.