Risk assessment for commercial crime and legal protection based on modularity-optimized LM and SCA-optimized CNN

Modularity optimization process

As an important index to measure the reasonable degree of community division, the main idea is in a random business network, the probability of capital transaction relationship between two accounts (that is, there are edges between two nodes) is equal. It has the same number of nodes as the actual network, but the edges in the random network are connected randomly. By comparing the proportion of the number of edges of each community node with the total number of edges in the actual network, subtracting the expected difference of the total number of edges in the community of the corresponding random network. If the difference is larger, the randomness is smaller, the relationship between nodes in the network is closer, and the situation of community division is better (Seifikar, Farzi & Barati, 2020). Therefore, we can define modularity as follows: (1)${\displaystyle Q=\frac{1}{2m}\sum _{i,j}\left|A_{ij}-\frac{k_i{k}_j}{2m}\right|\delta \left(c_i,c_j\right)}$ where m represents the number of edges in the network, A_ij represents the weight of edges between node I and node j, indicating the closeness between node i and node j. k_i is the sum of the values of all edges connected to node i, and $\frac{k_i{k}_j}{2m}$ represents the closeness of i and j when the network is random. c_i is the cluster number of node i. If c_j is the same, then $\delta \left(c_i,c_j\right)=1$, indicating that node i and node j are in the same cluster. Otherwise, $\delta \left(c_i,c_j\right)=0$, indicating that node i and node j are not in the same cluster. $\frac{1}{2m}$ is the introduced inertia factor, which is to control the value of modularity within the interval (0,1).

According to the idea of modularity, the definition of community modularity gain is given as follows: (2)${\displaystyle \delta Q=\left[\frac{\sum in+k_{i,in}}{2m}-{\left(\frac{\sum tot+k_i}{2m}\right)}^2\right]-\left[\frac{\sum in}{2m}-{\left(\frac{\sum tot}{2m}\right)}^2-{\left(\frac{k_i}{2m}\right)}^2\right]}$

The above formula can be simplified as (3)${\displaystyle \delta Q^{{}^{\prime }}=k_{i,in}-\frac{\sum tot\times k_i}{m}}$

whereas, k_i,in signifies the summation of weights about cluster C linked to node i, and ∑ tot symbolizes the cumulative sum of total weights connected to cluster C. Additionally, k_i denotes the cumulative sum of total weights linked to node i. It is noteworthy that the simplified calculation yields a relative gain rather than an absolute gain. This transformation significantly mitigates programming complexity.

As shown in Fig. 1, the application of the LM algorithm based on modularity in the scene of commercial crime identification is divided into two parts.

In the first part, each node in the financial network is regarded as an independent community, and these communities are classified by the above evaluation model of modularity and modularity gain, and similar communities are classified into one group and identified.

In the second part, we reinitialize the new network, merge multiple communities into a community, and then repeat the first part to complete a round of iteration. When the modularity Q of the whole network no longer changes after iteration (δQ → 0), the iteration stops.

Implementation process

The specific steps of the above algorithm are shown in Fig. 2.

(1) Each node in the transaction network is regarded as an independent community.

(2) After traversing each node of the transaction network, the nodes traversed are allocated to the community of adjacent nodes in turn, and the modularity gain of the whole network δQ is calculated if max(δQ) > 0, that is, there is an adjacent node of the current node. After merging the current node into a community, the module degree of the whole network increases, while if it does not exist max(δQ) > 0. The current node does not join the community where any node is located, and the original state remains unchanged (Zhang et al., 2021).

(3) Repeat Step (2) to determine that all nodes in the network have an optimal community so that the network modularity gain reaches the maximum value.

(4) In this way, all the nodes belonging to the same community are merged into one node. The weights of the edges between the nodes in the community are transformed into the weights of the new nodes, and the weights of the edges between the communities are transformed into the weights of the edges between the new communities.

(5) Repeat Step (1) until the modularity of the whole network is no longer changed; that is, there is no merging of any two communities so that max(δQ) > 0. At this time, the network remains relatively stable.

In traversing the intricate web of transaction nodes within the network, a systematic procedure is followed to determine the allocation of these nodes to their respective adjacent communities (Niu et al., 2023). This allocation step plays a pivotal role in assessing the community structure’s robustness and optimizing it for enhanced modularity, a key measure of network organization. At each juncture of node traversal, the algorithm assesses the potential benefit of reallocating the current node to a different community. This evaluation hinges on the concept of “modularity gain”, which quantifies the improvement in the network’s modularity when a node is moved to a new community. In this context, modularity measures how densely connected the nodes are within a community compared to what would be expected by chance.

In the implementation of the community discovery algorithm, the most complex and time-consuming task is the community division in step (2) because there are a large number of nodes participating in the calculation, and the modularity gain of the whole network needs to be calculated when the current node joins each neighbor node. In principle, the community division of each node can be optimized with the idea of parallelization because the modularity change is only related to the community of the current node and the neighbor node of the current node and has nothing to do with other communities. When step (2) is executed, the order of traversing nodes has little influence on the final community clustering effect (Linhares et al., 2020).

Overall design

Artificial intelligence technology can meet the needs of many judicial aspects, such as intelligent conviction, classification of legal advisory issues, document recommendation, etc. The task of intelligent conviction is to use the computer to read the case description and automatically give the appropriate charges. The classification task of legal consultation is to predict which legal level the problem may belong to based on the description of the user problem. The task of document recommendation is to search for similar documents from massive data to assist judges and lawyers in judging cases. Given the identification of commercial crimes, this article proposes a corresponding legal assistant decision-making model, as shown in Fig. 3. The model mainly solves two problems: one is crime prediction, and the other is the classification of legal advisory issues.

CNN algorithm design

Super parameter optimization

In this article, SCA is proposed to optimize the parameters, that is, to find the most suitable set of parameters in the range of optional parameters so that the model’s accuracy is the highest. In the operation of SCA, it is necessary to determine the fitness function. In this experiment, the accuracy of the model on the test set is selected as the fitness function, as shown in Eq. (7) (7)${\displaystyle \mathrm{acc}\left(f;D\right)=\frac{1}{m}\sum _{\mathrm{i}=1}^{\mathrm{m}}\mathrm{II}\left(\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)={\mathrm{y}}_{\mathrm{i}}\right)}$

To balance the exploration and development phases and the range of sine and cosine in the equation. The following equation is used for adaptive changes: (8)${\displaystyle {\mathrm{r}}_1=\mathrm{a}-\mathrm{t}\frac{\mathrm{a}}{\mathrm{T}}}$

where t is the current iteration, T is the maximum number of iterations, and a is a constant. The specific optimization steps are as follows:

(1) The processed and transformed data are divided into a test set and a training set, which are used for model training and testing. The hyper-parameter range of the prediction model was determined.

(2) Initialize SCA and set the parameters of SCA.

(3) Execute the first iteration of SCA, where the fitness value is calculated according to the fitness function, and the solution with the highest fitness in the current initial solution set is selected and saved.

(4) When t is 2, the parameter r1 is calculated and the position of the candidate solution is updated.

(5) After the new candidate solutions are obtained, the fitness of each candidate solution is calculated. The optimal fitness in this iteration is selected for comparison with the candidate solutions saved in the last round. If the current candidate solution is superior to the previous one, the current candidate solution is selected. Otherwise, the solution from the previous iteration is selected.

(6) Judge whether the termination conditions are met, and if so, proceed to the next step; Otherwise, make t = t + 1 and repeat Step (5) and Step (6).

(7) When the optimal fitness solution and the location of the solution are obtained, the hyper-parameters are output, and the parameters are input into the model for training to get the final model.

Experimental data

In this research endeavor, the experimentation process relied on authentic bank production data, underscoring the validity and practicality of the findings. The experiment was conducted meticulously and precisely, leveraging a genuine data set sourced from a banking institution. This data set, accessible at the following link (https://doi.org/10.7272/Q61G0JHJ), comprises a comprehensive and extensive collection of financial records.

To provide a snapshot of the data’s magnitude, it encompasses a staggering 78,760 distinct accounts, embodying a diverse cross-section of financial activity. Within the confines of a single month, an astonishing 568,978 transaction records were meticulously logged and analyzed. Each transaction record is replete with a rich tapestry of information, containing 70 distinct fields, each offering valuable insights into the intricate world of financial transactions.

It is imperative to note that the bank, in a conscientious effort to safeguard customer privacy and protect sensitive financial information, has taken stringent measures to ensure data security. Consequently, the real production data set has been transformed into a secure and confidential format. This transformation includes desensitization, which involves removing or obfuscating personally identifiable information, and encryption, which fortifies the data against unauthorized access. These measures collectively ensure that the integrity and confidentiality of the data are upheld, complying with the highest standards of data protection and privacy regulations.

By employing this authentic and rigorously prepared data set, the study aimed to provide a robust foundation for its analyses, insights, and conclusions. The reliance on actual production data enhances the relevance and applicability of the research findings, ultimately contributing to a deeper understanding of the intricate dynamics surrounding commercial network criminal gangs and their activities within the realm of capital transactions.

Model training effect

All the corpus was divided into 7:3 parts, 70% of which were used to train the model and 30% to verify the performance of the model. The fitness curves in the model training process are shown in Figs. 4 and 5, and accuracy is used to evaluate them.

As can be seen from the figure, the accuracy rate of the legal assistant decision model is maintained at 94%–95%, and that of the commercial crime identification model is maintained at 92%–93%. As the number of iterations increases, the fitness value will also increase. When the number of iterations reaches 25–30, the fitness value tends to be stable. After 50 iterations, the algorithm stops. Finally, the highest accuracy rate of the legal aid decision model is 95.93% and 93.66% of the commercial crime identification model.

Comparison of different models

The commonly used algorithm models are selected for comparison, and the comparison results are shown in Fig. 6.

The research outcomes unequivocally demonstrate the superiority of deep learning methodologies over traditional machine learning algorithms in commercial crime identification. This empirical evidence underscores the potential of advanced neural network-based techniques in tackling complex real-world challenges. Specifically, the deep learning approach exhibited remarkable performance gains compared to its traditional counterparts.

Notably, within the realm of deep learning, a significant enhancement in accuracy was observed with the utilization of an optimized CNN as opposed to a CNN with manually configured hyperparameters. This optimization process underscores the importance of fine-tuning neural network architectures to suit the specific task. By carefully tuning the hyperparameters, the algorithm achieved higher accuracy, further underlining the capacity for deep learning to adapt and excel in intricate problem domains.

Conversely, a stark contrast emerged when comparing deep learning, represented by CNN, with the traditional random forest algorithm. While the deep learning approach exhibited substantial advantages in terms of accuracy, it is essential to acknowledge that deep learning algorithms may not always yield ideal results in all scenarios. One key reason for this disparity is the nature of the legal consultation questions. These questions tend to be concise and lack substantial linguistic connections. Consequently, the deep learning algorithms face the challenge of discerning and classifying these short sentences, often relying on just a handful of crucial keywords.

In summary, these findings emphasize the evolving landscape of machine learning, where deep learning techniques are proving their mettle in specialized tasks like commercial crime identification. However, the data’s intricacies and the problem’s specific characteristics must be considered when selecting the appropriate algorithm. The unique challenge posed by succinct legal consultation questions highlights the importance of continuous refinement and adaptation in achieving optimal algorithmic performance.

Commercial crime identification effect

According to the suspicious report and the later investigation certificate, the commercial criminal account provided by the bank is taken as the real criminal account. The suspicious account in the scope of the real criminal account obtained by the algorithm in this article is regarded as the experimental suspicious account, and the account not within the scope of the real criminal account is regarded as the experimental false alarm account. In the commercial transaction network, the Adjusted Rand Index (ARI) is used to measure the accuracy of the results. The experimental results are shown in Fig. 7.

Figure 7 shows that the commercial crime identification model based on modular optimization proposed in this article can identify the criminal gangs in the commercial trading network, and the accuracy rate is more than 90%. When the fund transaction between accounts is characterized by low amount frequency, the model performs better because the intimacy weight between accounts becomes smaller and the number of suspicious accounts decreases, which indicates that the method meets the expectation and the experimental results are reasonable.