This article investigates an emerging social commerce model that integrates social networks and e-commerce, highlighting the pivotal role of topic marketing in influencing consumers’ purchasing decisions. Within the framework of user-generated content (UGC), and accounting for the complex interplay among factors influencing topic propagation as well as the cooperative and competitive dynamics between topics, this study proposes a marketing topic propagation model based on factor analysis and the Stackelberg game. First, factor analysis was employed to extract two primary factors influencing topic propagation—user behavior and external environmental factors—thereby reducing the dimensionality of the variables. A multiple linear regression model was subsequently applied to quantify the contribution of these factors, establishing a robust quantitative foundation for optimizing marketing strategies. Second, to account for the competitive and cooperative interactions among topics, the behavior of ordinary users and influencers was analyzed using a Stackelberg game framework. This analysis reveals the complex interdependencies between cooperative and competitive dynamics in topic propagation. Finally, to address the behavioral variability and time-varying nature of users’ active participation or neglect (of topics), the traditional susceptible-infectious-recovered (SIR) model was refined by subdividing the infectious state into “marketing” and “neglected” states, resulting in the susceptible-marketing-neglected-recovered (SMNR) dynamic propagation model. By incorporating a temporal dimension, the model captures dynamic changes in states and parameters during topic propagation, thereby enhancing the accuracy of predictions regarding propagation paths and trends. Experimental results demonstrate that the proposed model effectively measures dynamic changes in influencing factors, incorporates game-theoretic relationships, and accurately predicts the temporal evolution of marketing topics. Its dynamic characteristics provide a robust theoretical foundation for optimizing social commerce marketing strategies and offer precise guidance for data-driven marketing decisions.

In the context of social commerce, user dissemination behavior is influenced by the coupling of multiple factors, such as the timeliness of marketing content and the dynamics of social relationships. Existing methods are limited in predictive accuracy due to neglecting the cold-start data sparsity and the evolution patterns of behavior sequences. To address this issue, we propose a predictive model for user dissemination behavior in social commerce, leveraging transfer learning and sparse representation techniques. Firstly, to tackle the problem of sparse cold-start topic data, a cross-domain transfer learning framework is designed. Historical topics are matched as the source domain based on semantic similarity, and knowledge transfer is achieved through a domain adaptation loss function, thereby improving the model's performance for cold-start or low-engagement topics. Second, to address the challenge of high-dimensional feature modeling, a dual sparse coding method is proposed. This method performs low-rank decomposition on both the user attribute matrix and the social adjacency matrix, preserving core structural information while reducing computational complexity. Finally, to handle the dynamic propagation characteristics, a utility function combining tripartite game theory is constructed, incorporating the marketing content attractiveness, user social influence, and time decay factor. This is embedded into the weight generation module of the relationship-aware graph attention network. By using a dynamic time encoder, the evolution pattern of behaviors is captured, enabling accurate prediction of social commerce user behavior. Experimental results show that this model can not only accurately predict users' interactions with marketing topics but also reveal the dissemination patterns of marketing content, providing strong support for optimizing marketing strategies. This research offers an effective technical means for the precise placement of marketing content and user behavior analysis in social commerce.

In social networks, studying methods for predicting the popularity of malicious information can help improve the ability to predict online public opinion. This paper proposes a malicious information popularity prediction model based on user influence, targeting the cooperative adversarial nature of malicious information propagation, the problem of assessing user influence in malicious information propagation space, and the complexity of malicious information propagation space. First, regarding the cooperative adversarial nature of the malicious information propagation process, considering that user behavior is influenced by both malicious and positive information during the propagation process, evolutionary game theory and multiple linear regression are introduced, and internal and external behavioral factors of the user are synthesized to construct influential functions that quantify malicious information and positive information. Meanwhile, the influence matrix is introduced when quantifying information to construct a weighted malicious information propagation network further. Second, regarding the problem of assessing user influence in the malicious information propagation space, considering the advantages of PageRank in measuring the importance of web pages and combining the timeliness of malicious information propagation, an improved algorithm T-PageRank (Timeliness-PageRank) based on timeliness is proposed. Introducing the time decay factor into the PageRank algorithm effectively enhances the accuracy and timeliness of the influence assessment of malicious information propagation. Finally, regarding the complexity of the propagation space of malicious information and considering that Graph Attention Network (GAT) can effectively capture complex relationships between nodes, combined with user influence, a malicious information popularity prediction model based on GAT is constructed. The model learns the complex interaction between users by using GAT and updates the feature representation of users so that it can be used for subsequent malicious information popularity prediction tasks. The experiment shows that the model can not only accurately assess the influence of users but also effectively predict the popularity of malicious information propagation.