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.

翻译：本文提出连续时间分数主题模型（cFTM），一种用于动态主题建模的新方法。该方法引入分数布朗运动（fBm），能够有效识别主题和词汇分布随时间演变的正向或负向相关性，揭示长期依赖性或粗糙性。理论分析表明，cFTM可捕获主题分布与词汇分布中的长期依赖性或粗糙性特征，这与fBm的主要特性相吻合。此外，我们证明cFTM的参数估计过程与传统主题模型LDA相当。为验证cFTM的特性，我们采用经济新闻文章进行实证研究，实验结果支持该模型识别并追踪主题随时间变化的长期依赖性或粗糙性能力。