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Applying Crime Prediction Techniques to Japan: A Comparison Between Risk Terrain Modeling and Other Methods

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In recent years, the field of crime prediction has drawn increasing attention in Japan. However, predicting crime in Japan is especially challenging because the crime rate is considerably lower than that of other developed countries, making the development of a statistical model for crime prediction quite difficult. Risk terrain modeling (RTM) may be the most suitable method, as it depends mainly on the environmental factors associated with crime and does not require past crime data. In this study, we applied RTM to cases of theft from vehicles in Fukuoka, Japan, in 2014 and evaluated the predictive performance (hit rate and predictive accuracy index) in comparison to other crime prediction techniques, including KDE, ProMap, and SEPP, which use past crime occurrences to predict future crime. RTM was approximately twice as effective as the other techniques. Based on the results, we discuss the merits of and drawbacks to using RTM in Japan.

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  1. According to United Nations Office on Drugs and Crime (UNODC) statistics (, the number of police-recorded offenses per 100,000 people in the US and Japan in 2014 are as follows: for theft, 1818.46 vs. 356.20; for burglary, 536.28 vs. 73.79; for assault, 228.86 vs. 21.02; for robbery, 101.08 vs. 2.41; for rape, 36.95 vs. 0.99; and for intentional homicide, 4.43 vs. 0.31.

  2. While we do not discuss them here, we can find important studies that discuss the complexities of and tips for operationalizing hotspots in GIS (e.g., Chainey and Ratcliffe 2013; Eck et al. 2005). Other research discusses various techniques available for operationalization of hotspots (e.g., Haberman 2017). Crime prediction studies rely on this research, and thus the two are closely related.

  3. Original data were downloaded from Fukuoka Prefectural Police Department’s homepage (, Tokyo Metropolitan Police Department’s homepage ( and the FBI’s Uniform Crime Reporting website (; the rates were then calculated.

  4. We should be cautious when dealing with crime data since under-reported occurrences are always present. Although we cannot know whether current data from Fukuoka city omit these potential victimizations, we can show how much underreporting is present in Japan. According to the fourth National Crime Victimization Survey (, in Japan in 2014, 29.5% of VLT (excluding N.A.s) were not reported to the police.


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The data on crime was provided to us under the Fukuoka Prefectural Police’s Crime Prevention Research Advisor framework; we would like to thank the Fukuoka Prefectural Police for their support. We would also like to thank Dr. Millar for English language editing.


This study was funded by a grant from the Nikkoso Research Foundation for Safe Society in 2016 and JSPS Grant Number JP17H02046.

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Correspondence to Tomoya Ohyama.

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Description for ProMap

For ProMap, the bandwidth and cell size were set similarly to KDE. We estimated the intensity of crime in a location (s) on date (t), using Eq. 1.1, as formulated by Johnson et al. (2009).

$$ \widehat{\lambda}\left(t,s\right)=\sum \limits_{c_i\le \tau \cap {e}_i\le \nu}\left(\frac{1}{\left(1+{c}_i\right)}\right)\frac{1}{\left(1+{e}_i\right)} $$

where τ is the spatial bandwidth, ν is the temporal bandwidth, ci is the number of cells between each location of crime i within the spatial, ei is the time elapsed for each occurrence time of crime i within the temporal bandwidth bandwidth and the cell.

To obtain ci in Eq. 1.1, as shown in Fig. 4, a plurality of concentric circles (radius 12.5 m + 25 m*n, where n = 0, 1, 2, …, 10) were drawn. Although the radius of the largest circle is 262.5 m at the maximum, 250 m was set as the upper limit in order to exclude points outside of it. Equal weighting was given to the points existing within the same distance range (as shown in Fig. 4, X1 = 0, X2 = 1, X3 = 2). As in previous studies (Bowers et al. 2004; Johnson et al. 2007, 2009), the number of weeks from the date of occurrence was used for ei. The number of days was divided by 7; no rounding was performed.

Fig. 4
figure 4

Value of ci of ProMap in the current study

Description for SEPP

For SEPP, the prediction was carried out using Eq. 1.2 with reference to a series of studies by Mohler (Mohler et al. 2011; Mohler 2014, 2015). The intensity of crime in a location (x,y) on date (t) is described as:

$$ \lambda \left(t,x,y\right)=\sum \limits_{\left\{k:{t}_k<t\right\}}\mu \left(x-{x}_k,y-{y}_k\right)+\sum \limits_{\left\{k:{t}_k<t\right\}}g\left(t-{t}_k,x-{x}_k,y-{y}_k\right) $$

where t-tk is the numbers of dates between a prediction target period and each occurrence date of a crime event, x-xk, y-yk are the instance between each target cell and each crime event.

We estimated μ and g using Eqs. 1.3 and 1.4.

$$ \mu \left(x,y\right)=\frac{\alpha }{T}\sum \limits_{t_i<t}\frac{1}{2{\pi \eta}^2}\times \mathit{\exp}\left(-\frac{{\left(x-{x}_i\right)}^2+{\left(y-{y}_i\right)}^2}{2{\eta}^2}\right) $$
$$ g\left(t,x,y\right)=\theta \omega exp\left(-\omega \left(t-{t}_i\right)\right)\times \frac{1}{2{\pi \sigma}^2}\mathit{\exp}\left(-\frac{{\left(x-{x}_i\right)}^2+{\left(y-{y}_i\right)}^2}{2{\sigma}^2}\right) $$


$$ \alpha =\frac{\sum_{i=1}^{N_i}{\sum}_{j=1}^{N_j}{p}_{ij}^b1}{N_i} $$
$$ {\upeta}^2=\frac{\sum_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{i}}}{\sum}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{j}}}{p}_{ij}^b\left({\left(x-{x}_i\right)}^2+{\left(y-{y}_i\right)}^2\right)}{2{\sum}_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{i}}}{\sum}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{j}}}{p}_{ij}^b} $$
$$ \theta =\frac{\sum_{i=1}^{N_i}{\sum}_{j=1}^{N_j}{p}_{ij}1}{N_j-{\sum}_{j=1}^{N_j}\exp \left(-\omega \left(T-{t}_j\right)\right)1} $$
$$ \omega =\frac{\sum_{i<j}{p}_{ij}}{\sum_{i<j}\left({t}_j-{t}_i\right){p}_{ij}} $$
$$ {\sigma}^2=\frac{\sum_{i=1}^{N_i}{\sum}_{j=1}^{N_j}{p}_{ij}\left({\left(x-{x}_i\right)}^2+{\left(y-{y}_i\right)}^2\right)}{2{\sum}_{i=1}^{N_i}{\sum}_{j=1}^{N_j}{p}_{ij}} $$

In these equations, pij indicates the probability of event i (offspring) being triggered by another event j (parent). These i and j events are called triggering pairs. Additionally, pbij is defined as the probability that event i occurs independently from other events. Thus, i is called a background event (equal to the parent events). We divided events into triggering pairs and background events using the EM algorithm described by Rosser and Cheng (2016). First, we set initial values of pij following Eq. 1.8 (here, we set α as 1.5 and β as 500) and obtained the probability matrix P0 (upper triangular matrix). Based on those values, we distinguished parents and their offspring.

$$ {p}_{ij}=\mathit{\exp}\left(-\alpha \left({t}_j-{t}_i\right)\right)\mathit{\exp}\left(-\frac{{\left({x}_j-{x}_i\right)}^2+{\left({y}_j-{y}_i\right)}^2}{2{\beta}^2}\right) $$

We then calculated parameters following Eqs. 1.51.11. The ω and σ2 were computed using triggering pairs. Once we obtained the parameters, we updated pij following Eq. 1.11 and repeated these steps until ||Pn-Pn-1|| was smaller than 1 × 10−7.

$$ {p}_{ij}=\theta \omega exp\left(-\alpha \omega \left({t}_j-{t}_i\right)\right)\times \frac{1}{2{\pi \sigma}^2}\mathit{\exp}\left(-\frac{{\left({x}_j-{x}_i\right)}^2+{\left({y}_j-{y}_i\right)}^2}{2{\sigma}^2}\right) $$
Fig. 5
figure 5

Prediction maps using KDE (top left), ProMap (top right), and SEPP (bottom) from July to December

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Ohyama, T., Amemiya, M. Applying Crime Prediction Techniques to Japan: A Comparison Between Risk Terrain Modeling and Other Methods. Eur J Crim Policy Res 24, 469–487 (2018).

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