Optimizing Police Locations around Football Stadiums Based on a Multicriteria Unsupervised Clustering Analysis ^†

Abstract

This work proposes a methodology based on multicriteria decision aid (MCDA) and a cluster analysis to identify ideal locations for the installation of police facilities or vehicle parking and policing around stadiums in Recife, Brazil, during potential violent sports events (criminal occurrences from football supporters or fanbases). A K-means unsupervised clustering algorithm is used to group criminal data into homogeneous clusters based on their characteristics. Each type of criminal occurrence is linked to a single cluster. The optimal location is addressed based on the PROMETHEE method (Preference Ranking Organization Method for Enrichment Evaluation), allowing clusters to be organized into a hierarchy based on the number of facilities (N), the average distance (D) from the criminal occurrence to the associated cluster, and the coverage level (C), which is the proportion of crime occurring in a location less than 500 m from the associated cluster. Through a data analysis of crimes and violence in the region, this study seeks to identify patterns of criminal behaviour and high-risk areas to determine the most strategic locations for police units and enhance the public security decision-making process. The choice for the k parameters ranged from 1 to 30, incorporating all regions of the analysis, with a computational cost of 43 min of running time using an Intel Core i3-3217U (1800 GHz and 10 GB of RAM). This approach and methodology can be useful for supporting public security policies in the region and can contribute to reducing violence around stadiums. The empirical application can help guide public managers’ decisions regarding resource allocation and the implementation of more effective security policies, with the aim of ensuring a safer environment for fans and residents in the areas near stadiums.

1. Introduction

Football (soccer) is a social event that brings together people from different social, economic, and cultural backgrounds, representing a synthesis of multiple passions and objective and subjective determinations [1]. Nevertheless, not randomly, such events result in episodes of violence and misdemeanors in stadiums and their surroundings, especially in countries with a deep-rooted football culture [2]. Areas close to sports venues are often the scene of conflicts between rival fans, in addition to vandalism, theft, and other forms of violence. Some interesting works on the topic include [3,4] studies on the violent behavior of football supporters in Brazil.

The proper location of police units can be an important factor in preventing and reducing violence around stadiums. When there is a police unit close to the stadium, the police can act more quickly in case of conflicts or acts of violence. This can help ensure the safety of fans and residents in areas close to the stadium. Furthermore, a police presence can have a deterrent effect on potential offenders, reducing the risk of violence. This work seeks to identify strategic locations for installing police facilities, considering their quantity and using a hybrid spatial and multicriteria analysis method. In this work, a police vehicle containing up to four police officers is considered a police facility to provide more efficient and rapid responses to possible demands.

This work proposes a hybrid method using the PROMETHEE and K-means tools to identify possible strategic locations for installing police facilities depending on their quantity, improving public security and mitigating violence in regions around stadiums in Recife, Brazil. Such a hybrid method has a well-founded statistical base and is widely available in different languages and software. The justification for using unsupervised clustering is the need for an exploratory analysis without predefined labels or categories. In the case of crime data in Recife, defining explicit categories or classes may be challenging as criminal activities can be multifaceted and dynamic. In addition, unsupervised clustering methods are flexible and adaptable to different data types. In Recife, where several types of crimes are considered, this clustering approach identifies commonalities and differences across different crime categories and locations.

The next section offers a theoretical foundation for the employed methods. Section 3 is dedicated to the results and a discussion of the empirical application. Section 4 concludes the work with a summary of the results and discussion.

2. Methods

The facility location problem (FLP) is a topic of great interest in areas such as logistics, transport, and public service management where there is a need to decide where to install new service units or equipment. The objective is to decide in the best possible way where to locate a certain number of services to minimize costs and maximize the efficiency of the service provided [5].

The FLP is a complex problem involving several factors, such as the distance between facilities and customers, customer characteristics, facility capabilities, and the demand for services. The specialized literature presents several approaches to the solution of the problem, from mathematical models that seek an exact solution to the problem to heuristic algorithms that seek approximate solutions in a reasonable time. Many studies have considered methods to address the facility selection problem through the use of mathematical analyses and computer simulations [6].

The FLP solution can bring many benefits to society, such as improving the quality of services provided, reducing costs, optimizing resource distribution, and improving users’ well-being. Ideally, undesirable events (such as robberies, assaults, and vandalism) should be as far away from society as possible, but we have no control over them. Therefore, bringing desirable services closer to society is of interest. Many quantitative tools and information technologies are adequate for addressing socioeconomic issues and the problem of public security [7,8,9,10]. For the present study, the facility location problem is addressed by combining K-means clustering with multicriteria decision aid (the PROMETHEE model).

2.1. K-Means

K-means is a widely used unsupervised clustering algorithm for grouping data into homogeneous groups based on their characteristics. It is one of the most popular cluster classification algorithms due to its simplicity and efficiency [11].

This algorithm is iterative, starting with a random choice of k centroids representing each cluster’s center. Then, each data point is assigned to the cluster whose centroid is closest. Once all points have been assigned to a group, the centroids are recalculated based on the data points assigned to each group. This process is repeated until there are no more changes in assigning data points to groups or until the maximum number of iterations is reached.

Although K-means is a simple and fast algorithm, it has some limitations, such as sensitivity to choosing the number of k groups and the random initialization of centroids. However, there are techniques to deal with these problems, such as multiple random initialization and hierarchical sampling initialization. We combined this algorithm with the PROMEHTEE methodology for a more robust classification of vulnerable urban spaces.

2.2. PROMETHEE

The PROMETHEE method (Preference Ranking Organization Method for Enrichment Evaluation) is an approach that guides the decision-making process, allowing options to be organized in a hierarchy based on the preferences of the decision maker [12]. Developed by Brans et al. [13], this technique helps classify actions according to established criteria, allowing for a more precise and structured analysis of the available possibilities. Non-compensatory decision-making models such as PROMETHEE have been used well in the literature to evaluate job satisfaction and resource allocation [14,15].

The PROMETHEE method can be defined in two steps. In the first step, a comparison is made using preference functions of different types, such as difference functions and similarity functions. These comparisons generate a pre-order matrix that indicates the preference relationship between the alternatives in relation to each criterion individually. In a second step, the person responsible for making the decision assigns weights to the criteria according to priorities so that the most relevant criteria receive more significant weights.

It is necessary to assign weights to each criterion such that each criterion i must have a weight $p_i$. Thus, the degree of overclassification given by the equation can be calculated as follows:

$$\pi \left(a,b\right)={\displaystyle \sum }_{i=1}^n{p}_i{F}_i\left(a,b\right)$$

(1)

where

$n$ = decision criteria;

$\pi \left(a,b\right)$ = outranking of alternative a over alternative b;

$F_i$ = preference function for criteria $i$;

$p_i$ = weight for criteria $i$.

Based on the outranking degree of all alternatives, flows of alternatives can be calculated. There are three types of flow: positive flow, negative flow, and net flow. The positive flow ${\varnothing }^{+}\left(a\right)$ measures how much an action is preferred over the other n − 1 alternatives. Analogously, the negative flow ${\varnothing }^{-}(a$) tells us how preferable the n − 1 alternatives are. The net flow $\varnothing \left(a\right)$ subtracts the negative flow from the positive flow. This is basically how the alternative performs compared to the others. The greater the net flow, the more preferable the alternative. The equations used to calculate the flows are as follows:

$${\varnothing }^{+}\left(a\right)=\frac{1}{n-1}{\displaystyle \sum }_{b\ne a}\pi \left(a,b\right)$$

(2)

$${\varnothing }^{-}\left(a\right)=\frac{1}{n-1}{\displaystyle \sum }_{b\ne a}\pi \left(b,a\right)$$

(3)

$$\varnothing \left(a\right)={\varnothing }^{+}\left(a\right)-{\varnothing }^{-}\left(a\right)$$

(4)

3. Results and Discussion

The results of applying data-driven analytics and virtual learning technologies are crucial in optimizing resource provision and allocation, with valuable insights into the socioeconomic landscape [7,9,16]. By analyzing diverse datasets, including crime patterns, demographic information, and economic indicators, policymakers can make informed decisions to address specific challenges and allocate resources effectively.

The SEPLAG (State Planning and Management Secretariat) made available a database of CVP cases (property crimes) and their respective geolocations throughout Pernambuco. This base covers cases from 2018 to 2021 across the state. Among the crimes present in this database are thefts: theft occurring in bank institutions, theft on public transport, mugging and robberies, theft of cargo, burglary, and commercial burglary. See Nepomuceno and Costa [17], De Carvalho and Costa [8], and Borba et al. [18] for a better description of these geographic-referenced crimes and the context in which they operate.

Even without other types of crimes such as physical, sexual, psychological, or moral crimes, the existence of robbery data in general can be a useful indicator of occurrences of violence in urban areas. This is because robberies are often associated with acts of violence, such as physical aggression, threats, and intimidation. Figure 1 illustrates a plot of crimes in Recife through the ArcGis version 10.8 software, using OpenStreetMap as a base map.

The following Table,

Table 1. Proportion of CVPs (property crimes).

Types of CVPs	Arruda	Ilha Do Retiro	Aflitos
Robberies	13.5%	2.9%	6.7%
Mugging	76.9%	88.4%	81.3%
Burglary	3.8%	1.4%	0.0%
Theft and Robberies in Bus	3.8%	0.0%	1.3%
Commercial Burglary	1.9%	5.9%	10.7%
Theft and Robberies in Public Transport	0%	1.4%	0%

, reports the proportion of occurrences for each stadium based on the type of crime.

In order to minimize the problem of the initial choice of centroids, the multiple random initialization technique was adopted. This technique is the default in the Scikit library. The algorithm is executed with seeds from different centroids according to the specified number of times. The seed that generates the clusters with the smallest sum of the squared distances of the points to the cluster centroid is chosen. For this study, each cluster was executed with 5000 different seeds. This was achieved using a notebook equipped with an Intel(R) Core(TM) i3-3217U processor at a frequency of 1.80 GHz and with 10 GB of RAM memory, taking 1 hour and 43 minutes to complete.

Scenarios were created to identify the best allocation of facilities based on the number of facilities (N), average distance (D), and coverage level (C). The weights for each were provided by the ROC technique [19], considering the order of preference (under the criteria).

Table 2. Best alternatives in each scenario.

	Scenarios
Stadiums	1	2	3	4	5	6	Ranking
Aflitos	30 Locations	11 Locations	30 Locations	7 Locations	26 Locations	1 Local	1st
	26 Locations	10 Locations	29 Locations	8 Locations	28 Locations	2 Locations	2nd
	29 Locations	12 Locations	28 Locations	9 Locations	27 Locations	7 Locations	3rd
	28 Locations	13 Locations	27 Locations	10 Locations	29 Locations	3 Locations	4th
	27 Locations	14 Locations	26 Locations	1 Locations	30 Locations	6 Locations	5th
Ilha do retiro	30 Locations	10 Locations	30 Locations	7 Locations	30 Locations	1 Local	1st
	29 Locations	11 Locations	29 Locations	6 Locations	29 Locations	2 Locations	2nd
	28 Locations	12 Locations	28 Locations	8 Locations	26 Locations	6 Locations	3rd
	27 Locations	9 Locations	27 Locations	9 Locations	28 Locations	7 Locations	4th
	26 Locations	14 Locations	26 Locations	5 Locations	27 Locations	3 Locations	5th
Arruda	30 Locations	8 Locations	30 Locations	6 Locations	30 Locations	4 Locations	1st
	28 Locations	10 Locations	29 Locations	7 Locations	28 Locations	1 Local	2nd
	29 Locations	11 Locations	28 Locations	5 Locations	29 Locations	5 Locations	3rd
	27 Locations	7 Locations	27 Locations	4 Locations	27 Locations	6 Locations	4th
	26 Locations	9 Locations	26 Locations	8 Locations	26 Locations	7 Locations	5th

below reports the number of facilities (locations) for the five top-ranked alternatives for each stadium considering all six scenarios: the first scenario (C, D, N), second scenario (C, N, D), third scenario (D, C, N), fourth scenario (N, C, D), fifth scenario (D, N, C), and the sixth scenario (N, D, C).

4. Conclusions

The results report interesting prospects considering the three criteria and six options in order of preference (scenarios). Among the scenarios, only two obtained a balanced number of facilities. The remaining scenarios are not recommended options for a decision maker in any of the stages since these scenarios imply a high or insufficient number of facilities. Among the recommended scenarios at the Ilha do Retiro stadium, the second-best alternative solved the problem of intersections with rivers.

The proposed method has the advantage of simultaneously considering multiple criteria, such as socioeconomic factors, demographic data, and crime rates. This integration enhances the identification of patterns and relationships within crime data, aiding in comprehensive decision making for law enforcement and policymakers. Combining unsupervised clustering with multicriteria decision aid addresses subjectivity by balancing subjective criteria with data-driven insights. It also assists in identifying trade-offs in crime-prevention strategies and uncovers complex interactions within the data, leading to more effective crime analysis. This integration ensures a consistent and informed decision-making process in addressing crime challenges.

Applying this methodology in other Brazilian stadiums and considering other criteria not addressed in this work could be an interesting extension of the current analysis in addition to using data standardization to verify the impact on the generation of clusters. Furthermore, the possibility of applying a multicriteria system that serves multiple decision makers can also add value for the current approach.