Research on the regularity of network security crimes based on mathematical models

In order to address the current lack of universal research on network security issues in literature, and the absence of tailored research for different countries and regions, this paper conducts research using clustering analysis models, ARIMA time series prediction models, decision tree prediction models, and PLSR models. This article first collects data from authoritative platforms such as VCDB database to ensure the accuracy of input data, and then visualizes the data through heat maps to observe initial patterns. To verify the hypothesis, this paper adopts the K-means clustering model and uses the elbow rule to determine four clusters as the "elbow points" of the dataset. This article chooses GCI as the indicator for evaluating national policies. Considering the uniqueness of policy implementation, the data was normalized over time and the ARIMA model was used to predict the occurrence rate, while the decision tree model was used to determine the importance of each dimension. The results indicate that organizational measurement dimensions account for 88.5% of importance. Given that the data spans multiple countries and the sample data is limited, this article chooses to use the PLSR model together to alleviate this issue. Calculations show that GDP is the most closely related demographic feature to cybercrime, with an average value of 1.4202. Other demographic features show varying degrees of correlation.