Research on Dynamic Monitoring and Intelligent Early Warning of Community Correctional Recidivism Risk Based on Multidimensional Data Mining

With the study of multidimensional data cubes, the focus of association rules research has gradually changed from unidimensional data to multidimensional data. One of the most important concepts in multidimensional association rules is the concept of dimension, where people refer to analyzing a data cube from different perspectives as a dimension. A multidimensional association rule is a rule that involves multiple attributes or predicates. The relevant definitions are given below: 1)

Predicates for multidimensional data cube: Let a multidimensional data cube Cube be defined, then the dimensional predicate di is the predicate d_i ∈ D_i expressed in the following form.

Apriori algorithm is the most influential method for mining association rules in the field of association rules. The algorithm uses a priori knowledge of the nature of frequent itemset Apriori to explore the generation of candidate (K+1)-itemsets through a layer-by-layer iterative search method, where K-item frequent itemsets are used as a basis. First, the algorithm searches the set of frequent 1-item sets. This set is labeled as L1. Thereafter, the algorithm uses L1 to search for the set of frequent 2-item sets, L2. Then, L2 continues to be used to search for L3. This iterates until no frequent K-item sets can be found [21].

The algorithmic flow of Apriori is shown in Fig. 2, and the whole Apriori algorithm can be decomposed into the following two steps to design: 1)

Mining all frequent itemsets occurring in the relational database (R).

Frequent itemset means that the support of the item set is greater than the minimum support MinSupport.

Firstly, the relational database needs to be scanned to search for frequent 1-itemsets.

Then, a layer-by-layer iterative approach is used to search out frequent k-itemsets (k>1) from frequent k-1-itemsets, the specific design idea is:

After searching out the candidate frequent k-item set (Ck), the support of this candidate frequent item set is calculated, and then filtered according to the minimum support MinSupport to generate the frequent k-item set.

Search all frequent k-itemsets (k>0) by the above operation, and finally merge them all together.

Figure 2.

Flowchart of Apriori algorithm

The traditional Apriori algorithm is proposed for single-dimensional databases, and its running time will be greatly increased when the database data volume is very large and the support degree is very small, and at the same time, when generating frequent itemsets, the search space of candidate itemsets will be geometrically increased. The traditional Apriori algorithm requires a significant amount of computation when calculating the support of the item set. At the same time, the traditional Apriori algorithm repeatedly calculates the support of itemsets when generating association rules, without caching some intermediate calculations when solving the support of frequent itemsets. Finally, the traditional Apriori algorithm does not provide a clear solution when dealing with multidimensional data. Based on the shortcomings of traditional Apriori algorithms in dealing with multidimensional data, this paper proposes a MApriori algorithm based on the Mondrian platform.

The biggest improvement and the core of MApriori algorithm is to query Mondrian OLAP engine by constructing MDX statement to get the support degree of any item of multidimensional frequent predicate set, so as to determine whether the multidimensional predicate set is frequent or not.MDX can flexibly construct query expressions and dynamically generate multidimensional query results in the returned result set, which is a syntax specification specifically designed for retrieval on multidimensional data cubes. Therefore, in the MApriori algorithm, it is possible to manipulate multidimensional datasets using MDX statements to obtain multidimensional query results.

The complete MApriori algorithm flow is shown in Fig. 3 and its operational steps are as follows: 1)

Call the corresponding API provided by Mondrian to get each predicate of each dimension and its corresponding support, and save the predicate of support into Hash and put it into L1 at the same time.

Figure 3.

Flowchart of MApriori algorithm

This example takes the released and rehabilitated persons from a community correctional institution between 2018 and 2020 as a sample. First, {ethnicity, literacy, place of origin, marital status, offense, sentence term, age at release} are selected as condition attributes from the base data, and whether they recidivate or not is used as a decision attribute. Some of the condition attributes were merged (e.g., age at discharge = sentence termination date - date of birth) or deleted (e.g., deletion of irrelevant or similar attributes such as arresting authority, date of arrest, sentencing authority, and date of sentence).

Second, attribute values in the dataset were discretized and categorized. For example, the literacy level is discretized as {1: Elementary school and below, 2: Middle school, 3: High school (intermediate), 4: Specialized (high school), 5: Bachelor’s degree and above}. Charges are recorded through the code, itself is discrete, but in order to facilitate the analysis or need to go through some categorization (eg: 4002, 400201, 400202, 400203 respectively, “theft”, “habitual theft”, “attempted theft”). “Attempted burglary” and “preparation for burglary”, categorized and unified with 4002). Sentences are disaggregated into 1: less than 36 months, 2: 36-72 months, 3: 72-108 months, 4: more than 108 months}. The age at first offense is discretized as {1: under 25 years old, 2: 25 to 35 years old, 3: 35 to 45 years old, 4: over 45 years old}.

The discretized data were imported into Rosette and attributes were simplified using Johnson’s simplification algorithm, resulting in a simplified R = {education, offense, sentence, and age at diversion}, denoted as A, B, C, and D, respectively.

When the minimum support of MApriori algorithm is set to 0.3, the minimum confidence is set to 0.8, the minimum lift is 1, and the number of rule entries is 13, the results of multidimensional association rule mining are shown in Table 1, in which the code 4002 is the crime of theft.

In Table 1, the 1st rule is explained as: the number of offenders who committed theft with short sentences (less than 3 years) and low literacy (elementary school and below) accounted for 39.71% of the total sample data. At the same time 94.63% of these burglary offenders with short sentences have elementary school and below literacy. The degree of elevation (LIFT) indicates that this rule is more common than the finding that the first two conditions (committing burglary and having a low literacy level) are met at the same time.

In addition, the minimum support is set to 0.3, the minimum confidence is set to 0.6, and the minimum lift is 1. All the charges of community correctional officers are mined individually, and the results of multidimensional association rule mining are shown in Table 2. The “*” in parentheses in the table indicates the number of the charge in the prior criminal record.

As can be seen from Table 2, the current crime and the pre-crime record both contain the crime of theft, which accounts for 35.97% of the total sample data. Among the community ex-prisoners who committed the current offense of theft, 69.72% of the previous criminal records also contained the offense of theft. 60.38% of those whose prior criminal records contained a burglary offense committed a burglary offense in the present.

After using lift as a measure of relevance in the analysis, all positively correlated rules were filtered out, such as Rule 1 in Table 1, where Lift=2.1641 indicates that this rule is more common than finding that both of the first two conditions (committing a burglary and having a low level of literacy) are met. Similarly in Table 2 it is shown that neither rule is accidental and that it is more common than if it is found to have committed only one burglary offense. In addition, in Table 1, rules with some inclusion relationships are found which have the same successor (RHS) and the prior (LHS) is a subset of the relationship, for example, the LHS of Rule 2 contains the LHS of Rule 1, 3, 4, 5, 6, and 7, and the degree of enhancement of Rule 2 is greater than the degree of enhancement of the other rules, and these types of rules can be merged all together into Rule 2. Finally, based on the results, it can be seen that the cultural (elementary school and below), short sentence (less than 36 months), young age (less than 25 years old), and previous burglary are the main characteristics of reoffending, and the above results provide further support to the findings of the existing literature related to the analysis of the causes of crime. Table 2 shows that the crime of theft has its multiplicity and frequency. In view of the criminal characteristics of theft, community correctional institutions should strengthen the knowledge and skill training and psychological correction of community correctional personnel, and adopt a set of scientific and objective evidence-based correctional methods to prevent and reduce the likelihood of the recurrence of criminal acts of theft, and to improve their confidence and adaptability to return to society.

Logistic regression model is commonly used to describe the relationship between categorical response variables and explanatory variables, which belongs to a class of generalized linear regression models, and can be specifically divided into dichotomous regression models and multicategorical regression models [22]. Its explanatory variables can be continuous and discrete variables, such as attribute data, count data, etc., and the response variables are two or more discrete variables. In this paper, a bicategorical logistic regression model is used for monitoring recidivism risk in community corrections and early warning.

As a dichotomous logistic regression model, the response variable Y has only two outcomes such as “yes” or “no”, which are denoted by 1 and 0, respectively. Assuming that Y depends on p independent variables (or explanatory variables), which are denoted as X₁, X₂,…, X_p. Under the effect of p independent variables, the conditional probability of Y taking the value of “yes” is denoted as P = P_r {Y = 1 | X₁, X₂,…, X_p} = π(X), and the conditional probability of Y taking the value of “no” can be denoted as 1–P = P_r {Y = 0 | X₁, X₂,…, X_p} = 1–π(X), that is: 3P=π(X)=exp(β0+β1X1+β2X2+⋯+βpXp)1+exp(β0+β1X1+β2X2+⋯+βpXp)=11+exp[ −(β0+β1X1+β2X2+⋯+βpXp) ] 41−P=1−π(X)=11+exp(β0+β1X1+β2X2+⋯+βpXp)

Eq. (3) or Eq. (4) is also known as the general form of the Logistic regression model, where β₁, β₂,…, β_p is called the regression coefficient of the Logistic regression model and β₀ is called the constant term or intercept. From equation (3), it can be seen that the Logistic regression model is a typical probabilistic nonlinear regression model, where the independent variable X_j (j = 1,2,⋯, p) can be a continuous variable, a categorical variable, or a dummy variable. Notice that when the independent variable X_j (j = 1,2,⋯, p) takes on any value, β₀ +β₁ X₁ + β₂ X₂ +⋯+ β_p X_p takes on a range of (-∞,+∞), and therefore P always varies between 0 and 1, which is exactly what probability means.

Doing a logit transformation of equation (3), the logistic regression model can be transformed into the following linear form, i.e.: 5logit(P)=ln(P1−P)=β0+β1X1+β2X2+⋯+βpXp where P1−P is called the occurrence ratio of the event and is numerically equal to the ratio of the probability of the event occurring to the probability of the event not occurring.

Logistic regression models are nonlinear regression models, and the great likelihood method can be used to estimate the parameters of the nonlinear model. Since the response variable Y obeys a binomial distribution, then the probability distribution of Y ~ b(1, π(X)), and at this point E(Y) = π(X), one of the observations of the sample can be set as: 6P(yi|Xi)=π(Xi)yi[ 1−π(Xi) ]1−yi

Here X_i = [x_i1,x_i2,⋯, x_ip], i = 1,2,⋯, n, then the great likelihood function for the n sample observations is: 7L(β∣X,y)=∏i=1np(yi∣Xi;β)=∏i=1n[ π(Xi) ]yi[ 1−π(Xi) ]1−yi

The log-likelihood function is: 8l(β)=ln(L(β∣X,y))=∑i=1n{ yiln[ π(Xi) ]+(1−yi)ln[ 1−π(Xi) ] }

The Levenberg-Marquardt algorithm combines the advantages of Newton’s method and the gradient descent method and has a higher speed of iterative convergence. The specific procedure for iteratively solving the great likelihood estimation of β using the Levenberg-Marquardt algorithm is as follows:

Let the sample composition structure be: 9[ X,Y ]=[ x11x12⋯x1py1x21x2n⋯x2pyz……⋯……xn1xn2⋯xnpyn ]

Then, the log-likelihood function of the logistic regression model can be rewritten as: 10l(β)=∑i=1n{ yi(β0+β1xi1+⋯+βpxip)−ln[ 1+exp(βo+β1xi1+⋯+βpxip) ] }=∑i=1n{ yi(β0xi0+β1xi1+⋯+βpxip)−ln[ 1+exp(β0xi0+β1xi1+⋯+βpxip) ] }=∑i=1nyiβXi−∑i=1nln[ 1+exp(βXi) ] where x_i0 = 1, such that f(β)=l(β)=∑i=1nyiβXi−∑i=1nln[ 1+exp(βXi) ] , then: 11∇f(β)=∂f∂β,H(β)=[ ∂2f∂β02⋯∂2f∂β0∂βp⋮⋱⋮∂2f∂βp∂β0⋯∂2f∂βp2 ]

The iterative formula based on the principle of the Levenberg-Marquardt algorithm gives the iterative form of β as: 12βi+1=βi−(H+λD)−1∇f(βi) where H is the Hessian matrix, D is the diagonal matrix associated with H, and λ is the variable adjustment parameter. Given the initial value β₀ = {β₀₀, β₀₁,⋯, β_0p} and the computational accuracy ε, the iteration stops when ||β_i+1 – β_i|| ≤ ε, and a set of values for β_i+1, the corresponding parameter estimates of the logistic regression model, is obtained.

In constructing a community corrections recidivism early warning model using the Logistic regression algorithm, it is first necessary to preprocess the original dataset, divide the dataset into a training set and a test set in an appropriate proportion, and determine the independent variables (i.e., basic information attributes of community corrections personnel, crime information attributes, etc.) and dependent variables (i.e., recidivism status of community corrections personnel, “recidivism” is denoted as 1 and ‘non-recidivism’ is denoted as 0). Second, the training set was used to obtain the specific structure and regression coefficients of the regression model, and the test set was used to test the classification accuracy of the regression model.

Since in the logistic regression model, the output of Eq. (3) takes the value range of [0,1], which indicates the probability of community correctional officers reoffending, it is necessary to select an acceptable threshold of the probability of community correctional officers reoffending in practical applications, such as taking the threshold equal to 0.5, that is, when the output probability of the model is greater than 0.5, it is determined that the community correctional officers are in the state of recidivism, otherwise it is determined that the community correctional officers are in the state of recidivism. Otherwise, the community correctional officer is judged to be in a non-reoffending state.

The data samples used in this chapter were collected by collecting cases of crimes sentenced to community corrections in L state between 2018 and 2022 in the China Judgment Network and comparing the statewide community corrections personnel control database and the statewide offender management system with the support of L state community corrections agencies, from which the information of 600 offenders sentenced to community corrections in L state between 2018 and 2022 was extracted as the sample data, and based on whether they are first-time offenders and recidivists, divided into two groups of 294 samples in the recidivist group and 306 samples in the first-time offender group for comparison, and carried out a model fit test on the samples, and there were no missing value situations.

When the chi-square test was conducted on the elements affecting the likelihood of recidivism of community corrections officers, it was found that this independent variable was deleted because the p-value of community corrections officers’ criminal organizing was greater than 0.05, which was not statistically significant. At the same time, because this calculation started from the full model using the posterior progression method, that is, all independent variables of this model plus statistics were analyzed and evaluated one by one and the explanatory variables in the model that were not valid for it were removed, the variable of marital status was actively deleted during the analysis. And then extracted gender, cultural level, criminal experience and other seven factors that may have a more significant impact on the occurrence of recidivism of community correctional officers, combined with the results of Logistic regression analysis of the explanatory variables and the explanatory variables can be concluded that the seven factors on the possible triggering of recidivism of drug-involved personnel have different degrees of influence, so this paper through Logistic regression analysis The results were plotted in a multi-factor analysis table of influencing community correctional officers’ recidivism as shown in Table 3.

In Table 3, the meanings of the indicators are: β is the standardized partial regression coefficient, SE is the standard error of the partial regression coefficient, Wald is the value calculated in the chi-square test, OR is the ratio ratio, the dominance ratio, and P is the probability of the statistical observation. Statistics according to the significance of the test method of P-value is divided into three ranges of 0.001-0.01-0.05, it is generally believed that P-value of less than 0.05 indicates that the variables are statistically different, P-value of less than 0.01 indicates that there is a statistically significant difference between the variables, P-value of less than 0.001 (shown in the table as 0.000) indicates that the variables have extremely significant statistical differences. The probability of sampling error being the cause of the difference between the samples is lower than 0.05, 0.01, and 0.001.

Based on the selected sample data, each parameter was estimated using the Logistic regression model and combined with statistical significance (P<0.05), which in turn led to the establishment of a model equation for the early warning model of recidivism for community correctional officers to monitor the risk of crime and early warning for community correctional officers.

Combining the results of the analysis in Table 3 can visualize whether the coefficients of the regression equation are significant or not, and also test out the existence of covariance and other problems. As can be seen from Table 3, the meaningful variables are: gender χ₁, age 30-39 group χ₍₂₎₍₂₎, 40-49 group χ₍₂₎₍₃₎, 49-59 group χ₍₂₎₍₄₎, 60 and above group χ₍₂₎₍₅₎, place of residence χ₃, state of residence χ₄, junior high school educational level χ₍₅₎₍₂₎, high school educational level χ₍₅₎₍₃₎, occupation χ₆, experience with drug use χ₍₇₎₍₁₎. The final equation of the community corrections recidivism early warning model obtained is: 13Logit(p)=2.61−0.98χ1+0.33χ2(2)+0.31χ2(3)−4.41χ2(4)−17.95χ2(5)−0.38χ3−3.04χ4−0.91χ5(2)−0.82χ5(3)+0.92χ6+1.36χ7

The constructed early warning model of community correction is analyzed, and the content and results of the analysis are as follows: 1)

According to analyzing the variable of gender, it can be concluded that the β-value of gender as female is -0.98<0, P=0.005<0.05, which can be seen that the female group of community correctional personnel who are likely to commit recidivism among first-time offenders are less risky compared to the male group.

Based on the above analysis, in the community corrections recidivism early warning model equation, if the calculation results in a value closer to 1, it means that the community corrections officer has a higher probability of committing recidivism. On the contrary, if the result is closer to 0, it means that the community correction officer has a lower probability of committing reoffending.

Based on the community correctional personnel recidivism early warning model equation derived from the analysis of this paper, this paper selects two community correctional personnel for the following examples: 1)

When M is a male, 42 years old, living in the rural area, with a fixed residence, junior high school education level, unemployed, and has experience in drug abuse. According to M’s personal information, the early warning model equation can be utilized for calculation i.e. Logit(p)=2.59+0.31-3.04-0.91+0.92+1.36=1.23, and it can be seen that the result of the calculation is relatively close to 1, which indicates that the risk of the community correctional officer’s recidivism is relatively large.

Density-based clustering (DBSCAN) is a density-based clustering algorithm that identifies clusters by discovering high-density regions in a dataset and is effective in dealing with noise and outliers [23]. Following are the main concepts of DBSCAN:

CorePoints: refers to a data point in a dataset that satisfies the condition of containing at least MinPts of data points within a given neighborhood radius (Eps). In general, the core object is a high density point in the dataset with a sufficient number of neighboring points that can be approximated as the center of the clusters.

Directly Density-Reachable: Refers to a data point A If it is in the eps neighborhood of data point B and data point B is the core object, then it can be said that data point A is in a cluster with B as the core object. This means that with core object B, data point A can go directly to the cluster in which it resides.

Density-Reachable: means that for data points A and B, if there exists a sequence of data points P₁, P₂,……,P_n, where P₁ is A and P_n is B, and for each data point P_i(1 ≤ i ≤ n), P_i+1 in the sequence is within the neighborhood of P_i, then it can be said that data point A is within a cluster with data point B as the core object.

Density-Connected: if there exists data point C such that data points A and B are both within the Eps neighborhood of data point C, then data points A and B can be said to be within the same cluster.

The basic steps of DBSCAN algorithm are as follows: Step 1:

Initialization

Each object in the dataset needs to be given a category tag with an initial value of zero. When the category tag of an object is zero, it means that the object has not been categorized yet. Also initialize the parameters of the algorithm such as neighborhood radius (Eps) and neighborhood density threshold (MinPts).

The principle of DBSCAN algorithm is shown in Fig. 4, assuming that Eps is 3 and MinPts is 3, i.e., if the number of elements in the circle with Eps as the radius is 3, then the point is a core point. The dots within the circle in the figure indicate the core points, the triangles indicate the boundary points, and the squares indicate the noise points.

Figure 4.

DBSCAN schematic diagram

The basic idea is to determine the neighborhood radius of the elements in the sample data set and the minimum density threshold of the elements. Any one element is selected with Eps as the radius, if the number of elements in the circle is not less than the minimum density threshold, this element is the core point, the other elements in the circle are called boundary points, and the remaining elements are called noise points. According to the set parameters, the core point is found and the clustering is expanded based on the core point until all the elements in the dataset are traversed.

The performance of DBSCAN is directly affected by two key parameters, the neighborhood radius Eps and the neighborhood density threshold MinPts, which may cause large errors if the values of these parameters are not reasonable. The traditional manual parameter adjustment method can be hampered by subjective factors and may not be able to locate the optimal parameter combination. And DBSCAN may be less effective in dealing with clusters with large density differences, and it is easy to misidentify clusters with smaller density as noise points, which leads to bias in clustering results.

For this reason, this paper proposes a method for multi-density adaptive determination of the parameters of the DBSCAN algorithm. The algorithm is effective in handling community corrections recidivism datasets with large differences in density distribution. By identifying community corrections recidivism types with different densities, it can better adapt to the distribution characteristics of the community corrections recidivism dataset itself. Its adaptive nature makes the algorithm more flexible and stable in the process of clustering community correctional recidivism.

The key to the multi-density adaptive DBSCAN is based on the self-attenuating K – mean nearest neighbor algorithm and the mathematical expectation method, which is capable of automatically generating clustering parameters based on the characteristics of the community corrections recidivism dataset itself. Its specific steps are as follows: Step 1:

Calculate the Euclidean distance from each community corrections recidivism type to other community corrections recidivism types and generate the distance matrix Dist_m×m: 14Distm×m={ dist(a,b)|1≤a≤m,l≤b≤m } where m is the number of data sets, dist(a,b) is the Euclidean distance between points a and b, and Dist_m×m is a real symmetric matrix of order m.

After obtaining the list of neighborhood radius and density threshold parameters the parameter pairs corresponding to different k values are sequentially substituted for clustering (1 ≤ k ≤ m) and when the number of clustered clusters N is the same or converges several times in a row, it is the optimal number of clusters.

When the clustering result tends to be stable, its corresponding optimal parameters are selected in reverse order. In this paper, the number of consecutive stable times m is introduced to indicate the situation that the clustering results keep the same number of clusters: when the same number of clusters occurs m times consecutively, it means that the clustering results tend to be stable, and the number of clusters corresponding to the first stable interval will be labeled as the optimal number of clusters. If we cannot find the same number of clusters for m consecutive times, we will continue to search for the same number of clusters for m–1 consecutive times until we find a stable interval where the fluctuation of the number of clusters is within the range of one.

After determining the stabilization interval, the beginning of the interval is found at point starK and the end of the interval at point endK. In order to satisfy the need for accurate discrimination of the noise level, three noise levels are used in this paper, namely L (less noise), M (more noise) and N (normal noise). The following formula is used: 20K={ startK,level=M(startK+endK)2,level=NendK,level=L

Under the premise of ensuring correct clustering results, the lower the density threshold, the better the clustering effect. Calculate the density threshold under different k values, and under the premise of stabilizing the number of clusters, the minimum density threshold is obtained and recorded as the initial density threshold. The noise data under the initial density threshold is extracted and the same operation is performed to obtain a new density threshold until the number of noise data does not meet the minimum number of noise, and the clustering results of different density thresholds are combined.

In order to achieve the prediction of recidivism behavior of community correctional officers, this chapter explores the prediction mechanism of criminal behavior. The dataset used in this chapter is reliable and authentic data obtained from the public security authorities in District H. The dataset was used in the experiment. The dataset contains a total of eight attributes, and the experiment applied five attributes: crime type, location, date, latitude, and longitude for the study of crime prediction. One of the data for the year 2022 was selected for one year systematic analysis. In processing the data, the missing and doubtful data were removed and the valid data obtained was 1926. In the treatment of time, the time of occurrence of the case is taken as the month and day, such as June 15, 2022, which is taken as 6.15, which helps in the later DBSCAN experiments.

The relationship between the type of crime and the time of crime can be obtained intuitively through preliminary descriptive statistical analysis. Among the 1,926 crimes that occurred in District H in 2022, the main types of crimes are theft, fighting, drugs, gambling, obstruction, intentional injury, traffic collision, prostitution, extortion, dangerous driving, sexual assault, provocation and fraud in 13 major categories. The number of occurrences of different crime types is shown in Table 4.

According to the data in Table 4, analyzed from the perspective of crime types, among them, theft, fraud and dangerous driving are the three major crimes, accounting for 36.92%, 31.62% and 9.87% of the total number of crimes in the region for the whole year, respectively, and local public security authorities should pay attention to these three types of crimes. Analyzing from the perspective of the time of occurrence of crimes, May, June, and July are the time periods of high incidence of crimes. The high incidence time periods for theft-type crimes were January, April, June, and October, for fraud-type crimes were May, June, and July, and for dangerous driving crimes were May and June. Combining the characteristics of the type of crime and the time of the crime, the public security authorities should strengthen the control of theft-type, fraud-type and dangerous driving-type crimes in May, June and July, so as to effectively control the total number of crimes in H district.

Visualization techniques allow the presentation of statistical results. The different types of crimes are plotted in both temporal and spatial dimensions on a three-dimensional map, as shown in Figure 5.

Figure 5.

The spatial and temporal distribution of the type of crime

As can be seen from Figure 5, theft has the widest spatial and temporal distribution in the district, and it is clear that economic crime has become the type of crime that seriously affects the sense of security in the lives of the people in the district. Theft crimes are more concentrated in a specific spatio-temporal area, which ranges from latitude: 31°70′N to 31°75′N. longitude: 122°40′E to 122°50′E. time range: June to October. Thus, researchers can take preventive measures based on the types of crimes that frequently occur in an area during a certain time period. For example, if burglary cases are frequent in April to June and dangerous driving cases are frequent in August to October in Township c, District H, then community patrols can be strengthened in April to June, and more traffic policemen can be assigned to the roads in August to October, while focusing on the promotion of safe driving.

The correlation pattern of crime type and crime time can be found in the previous descriptive statistics, but more factors need to be considered for crime prediction. In this section, a crime prediction model based on the DBSCAN algorithm is constructed, and the crime type, crime location, and crime time are clustered and analyzed.

The results of clustering experiment of DBSCAN algorithm are shown in Figure 6. As can be seen from Fig. 6, five clusters are formed after clustering the crime data, indicating that the points in these five clusters are closely related in space and time. The higher the density, the higher the risk of crime in that area during that time period, and more police force should be allocated. It can be seen that there are five crime hotspots in District H in terms of crime time and space, and these five crime hotspots are mainly concentrated in one area: latitude 31°75′N~30°90′N, longitude 122°40′E~122°60′E. The public security organs should assign police force to this area as the core to spread to the periphery.

Figure 6.

DBSCAN algorithm clustering experimental results

If a continuous crime occurs in an area, the exclusion and attenuation zones around the actual residence can be identified by means of density clustering, which leads to the distribution of possible residences of the suspects and helps the police to narrow down the scope of investigation of the case. In addition, the model can monitor crime dynamics in real-time, update crime hotspots, conduct tracking investigations and research on long-term crime problems, and assess the effectiveness of policing prevention and control through changes in density. As for community correctional institutions, this model can also be used to predict crime among community correctional personnel, using the community where they serve their sentences as a space to predict recidivism.