Modeling and Predicting Popularity Dynamics of Microblogs using Self-Excited Hawkes Processes

Abstract: The ability to model and predict the popularity dynamics of individual user generated items on online media has important implications in a wide range of areas. In this paper, we propose a probabilistic model using a Self-Excited Hawkes Process(SEHP) to characterize the process through which individual microblogs gain their popularity. This model explicitly captures the triggering effect of each forwarding, distinguishing itself from the reinforced Poisson process based model where all previous forwardings are simply aggregated as a single triggering effect. We validate the proposed model by applying it on Sina Weibo, the most popular microblogging network in China. Experimental results demonstrate that the SEHP model consistently outperforms the model based on reinforced Poisson process.

• The paper presents a Self-Excited Hawkes Process model that quantifies each forwarding's contribution to the overall popularity dynamics of microblogs.
• It employs survival theory and an exponential decay factor to forecast the total number of forwardings, outperforming traditional Reinforced Poisson Process models.
• Experimental validation on Sina Weibo data demonstrates improved prediction accuracy and reduced error metrics, highlighting its potential in digital marketing and sociobehavioral research.

Modeling and Predicting Popularity Dynamics of Microblogs Using Self-Excited Hawkes Processes

Introduction

The challenge of predicting the popularity of User Generated Content (UGC) on social media platforms has significant implications across various fields such as viral marketing and public opinion assessment. This study focuses on developing a nuanced approach to modeling and predicting the popularity dynamics of microblogs, addressing the limitations of previous methods that neglect the distinct impact of individual forwarding actions. The paper introduces a probabilistic model based on Self-Excited Hawkes Processes (SEHP), which strategically quantifies each forwarding's contribution to the overall popularity cascades observed in microblogging environments, using Sina Weibo as a case study.

The Self-Excited Hawkes Process Model

The SEHP model characterizes the popularity dynamics of microblogs as a sequence of forwardings over time, denoted by time stamps during the period $[0, T]$. The model uses a rate function that incorporates both the initial attractiveness of the microblog and the cascading effects of each forwarding with an exponential decay factor. This formulation provides a flexible framework to capture the temporally recursive nature of online popularity dynamics, setting it apart from the Reinforced Poisson Process (RPP) models which aggregate effects into a mere singular magnitude.

The mathematical formulation of the SEHP involves defining a likelihood function based on survival theory principles, where forwardings during sequential intervals are statistically independent. Parameters such as initial and cascade-triggering strengths are estimated via maximum likelihood estimation, ultimately allowing the SEHP model to predict the expected total number of forwardings at any given time.

Experimental Validation

The efficacy of the SEHP model is tested on a dataset from Sina Weibo, restricted to microblogs with significant forwarding activity within specified timeframes. Comparative analysis with the baseline RPP model revealed that the SEHP model consistently delivers superior performance regarding prediction accuracy and error minimization. The paper employed Mean Absolute Percentage Error (MAPE) and a defined accuracy metric to quantify prediction outcomes, demonstrating substantive improvements in the SEHP model as evidenced by experimental results on error and accuracy forecasts over specified prediction windows.

Conclusions

The research presented details a sophisticated model for evaluating and forecasting the popularity growth of microblogs through SEHP, providing a marked improvement over existing RPP-based methodologies. These advancements not only heighten the tactical understanding of social media dynamics but also represent a significant step forward in leveraging stochastic processes for practical applications in predictive analytics. Future work may extend these findings by exploring adaptive models that further integrate user interaction complexities and network influence nuances for a more comprehensive understanding of digital content dissemination patterns.

Conclusion

The application of SEHP to microblog popularity metrics exemplifies a robust framework for capturing the intricate dynamics of information diffusion in social networks. By advancing these methodologies, the paper lays the groundwork for more nuanced and accurate prediction systems that can inform practices in digital marketing and sociobehavioral research. Continued exploration into model adaptations and broader social media contexts may yield further insights into the multifaceted field of online content influence and dissemination.