In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in topic and word distribution over time, revealing long-term dependency or roughness. Our theoretical analysis shows that the cFTM can capture these long-term dependency or roughness in both topic and word distributions, mirroring the main characteristics of fBm. Moreover, we prove that the parameter estimation process for the cFTM is on par with that of LDA, traditional topic models. To demonstrate the cFTM's property, we conduct empirical study using economic news articles. The results from these tests support the model's ability to identify and track long-term dependency or roughness in topics over time.

本文介绍了连续时间分数主题模型（cFTM），这是一种新的动态主题建模方法，它利用分数布朗运动（fBm）有效地识别时间上的主题和词分布的正向或负向相关性，揭示出长期依赖或粗糙性。我们的理论分析证明了cFTM可以捕捉主题和词分布中的这种长期依赖或粗糙性，反映了fBm的主要特征。此外，我们证明了cFTM的参数估计过程与LDA（传统主题模型）的相当。为了验证cFTM的性能，我们使用经济新闻文章进行了实证研究。这些测试的结果支持该模型在跟踪主题的长期依赖或粗糙性方面的能力。

CFTM：连续时间分数主题模型