## 2 Materials and Methods
### LDA Subject Modeling  
LDA is generative probabilistic model [15] pioneered by [PERSON], [PERSON], and [PERSON] in 2003 for revealing potential topics in textual data. The creation of LDA has brought significant progress in textual topic modeling. With the popularity of social media, the importance of textual data is increasing, posing new challenges to social science researchers. LDA models are widely used in social science research, including topic discovery and document categorization, due to their ability to extract topics from large amounts of text effectively.  
Figure 4 depicts the LDA topic model framework.  
The LDA model corresponding to Figure 4 has two main generative processes:  
1. \(\alpha\rightarrow\theta_{d}\to Z_{dn}\): In the LDA model, this process describes the generation process of the \(n\)th word in document \(d\). First, the topic distribution \(\theta_{d}\) of document \(d\) is extracted from the Dirichlet distribution based on the hyperparameter \(\alpha\), which represents the mixture of document topics. Then, the \(n\)th word in document \(d\) is assigned its attributable topic \(Z_{dn}\) based on \(\theta_{d}\). This process synthesizes the distribution of document topics and the distribution of vocabulary under each topic to ensure the appropriate matching of vocabulary and topic.
2. \(\beta\rightarrow\varphi_{k}\to W_{dn}\): In the LDA model, this process describes the generation of the \(n\)th word in a document \(d\). First, \(k\) topic-word distributions are obtained by sampling from the Dirichlet distribution based on the hyperparameter \(\beta\). Subsequently, the topic \(Z_{dn}\) of the \(n\)th word in document \(d\) is determined, and the appropriate vocabulary \(W_{dn}\) is generated for the word based on the corresponding topic-word distribution \(\varphi_{k}\). This process effectively captures the association between vocabulary and topic and realizes the topic modeling of textual data. The key point is to determine the topic for each word in the document through the topic-word distribution and then generate the corresponding words. Where the joint distribution of all variables is shown in Equation (4):  
Figure 4: Diagram of LDA subject model.  
\[p(w_{d},\ Z_{d},\theta_{d},\phi|\alpha,\beta)=\frac{N_{m}}{n=1}\ p(w_{dn}|\varphi_{ Z_{dn}})p(Z_{dn}|\theta_{d})p(\theta_{d}|\alpha)p(\phi|\beta) \tag{4}\]  
\(W_{dn}\) in Equation (4) represents the \(n\)th word in the \(d\)th document, which is a key concept in text data analysis. Text data is the object we want to analyze and mine, while the parameters \(\alpha\) and \(\beta\) are pre-set values that have a guiding role and affect the generation of topics and vocabulary. Except for the observable lexical variable \(W_{dn}\) and the a priori parameters \(\alpha\) and \(\beta\), other variables in the LDA model are hidden. Among these hidden variables, \(Z_{dn}\) denotes the topic to which the \(n\)th word in a document belongs, \(\theta_{d}\) denotes the topic distribution of document \(d\), and \(\varphi_{k}\) denotes the vocabulary distribution of the \(k\)th topic. LDA establishes the link between a document and a topic by inferring these hidden variables through analyzing textual data [16]. The model uses methods such as Bayesian inference for parameter estimation and learning to capture the topic structure and semantics of text to support text analysis and applications.  
The most commonly used parameter estimation methods for LDA probabilistic subject models include Gibbs Sampling [17] and Variational Inference [18]. Compared to Variational Inference, Gibbs Sampling is a simple and intuitive Markov Chain Monte Carlo (MCMC) method [19] for sampling hidden variables and parameters from a joint distribution, which can accurately sample from the posterior distribution to obtain accurate parameter estimates. In the LDA model, Gibbs sampling can update the estimates of the model parameters step by step by sampling each variable given the other variables. Therefore, Gibbs sampling is used in this paper to construct the LDA model.