## 4 Problem Formulation and Methodology
### Proposed Methodology
#### 4.2.2 Topic Modeling
\[p(a|s)=\frac{df(a|s)}{df(s)} \tag{2}\]  
\[U(a,t)=\frac{1}{|S_{t}|}\sum_{s\in S_{t}}p(a|s) \tag{3}\]  
\[U_{n}(a,t)=max(\frac{U\left(a,t\right)}{\sum_{t}U\left(a,t\right)}-\frac{1}{T },\ 0) \tag{4}\]  
\[a,t=\frac{Un(a,t)p}{1-p+Un(a,t)} \tag{5}\]  
\[\frac{n_{-i,t}^{(d)}+\alpha}{\sum_{u}^{t}n_{-i,u}^{(d)}+\alpha}\times\frac{n_ {-i,t}^{(w_{i})}+\beta}{\sum_{u\
eq}^{W}(n_{-i,t}^{(w)}+\beta)} \tag{6}\]  
Subsequently, the SLDA algorithm generated the topics using the Gibbs sampler based on the generative process stated in Algorithm 1. In the Gibbs sampling process, the conditional probability of a term \(a\) in \(d\) is computed based on (6), where \(n_{-i,t}^{(d)}\) is the number attributes in \(d\) assigned to topic \(t\), and \(n_{-i,t}^{(w_{i})}\) is the number attributes in whole corpus assigned to topic \(t\). Although the application of the Gibbs sampler is prevalent in LDA-based topic modeling experiments [7], our implementation is unique on the part of the documents where they are unlabeled and restricted to assess the topics in the perspective of psycholinguistics. Although the experiment using unlabeled documents will accelerate the constraints of sampling space [6], we were optimistic that the Gibbs sampler could improve the whole learning process and approximately estimate the \(t\) by leveraging the concealed knowledge and topical decomposition channeled through \(s\) and its associated \(t\) from respective \(S\). Intuitively, our team made the inference as the social network texts usually shorter and succinct with less contextual information [7; 50], would be structurally and semantically less complex than long texts [6]. In order to integrate \(S\) into the Gibbs Sampler, we defined \(\xi\) as the distribution of seeds \(S\) and applied Symmetric Dirichlet prior for \(\theta\), and \(\varphi\) with hyperparameters \(\alpha\), \(\beta\) and Dirichlet smoothing \(\gamma=0.01\). During the sampling process, we set the Markov Chain states for the latent topics \(t\) using multinomial distribution, \(\theta=p(t|\,\alpha,\gamma)\), where the computation controlled by \(\alpha\) in the \(d,\alpha=p(t|d)\). On the other hand, the conditional distribution of \(a\) and \(s\) derived through \(p\left(a|t,\ \beta,\gamma\right)=\pi_{\text{ai}}|T\), \(\pi_{\text{Si}}|T\), which controlled by \(\beta\) that determines the number of times a is sampled from the \(t\), prior to observing the words in \(d,\ \beta=p(a|t)\)[49]. The parameter \(\pi\) controls the probability of drawing a word from the seed topic distribution versus the regular topic distribution. We used the parameter values of \(1.0\) and \(0.1\) for \(\alpha\) and \(\beta\), respectively, as they showed insignificantly better modeling than the other values based on weights (5). The Gibbs sampler will approximately estimate the parameters and assign the high probable predefined topics from \(S\) by assuming that each \(a_{i}\) has their topic distribution of \(T=\{t_{1},\,\ldots,\,t_{n}\}\), where the \(n\in\mathbb{N}\) restricted to \(2\) and \(3\) denoting the number of \(t\) in one vs. all and multiclass distribution, respectively. The procedure to generate the topics depicted in Algorithm 1 and the descriptions about the notion stated in Table 3.  
```
For each topic \(t=1\ldots n\), choose \(\theta_{i}\) : Draw the regular topic \(\varphi_{t}^{\prime}\sim\text{Dir}\left(\beta_{r}\right)\). Draw the seed topic \(\varphi_{t}^{\prime}\sim\text{Dir}\left(\beta_{s}\right)\) Select \(\pi_{t}\sim\text{Beta}\left(1,1\right)\) For each seed set \(S\in\{1,\ \ldots,\ k\}\): Draw \(a\) distribution over seeds \(\xi t,S_{k}\sim\text{Dirichlet}\left(\gamma\right)\) For each document \(d\in\{1\ldots d\}\): Draw \(\theta_{d}\sim\text{Dir}\left(\alpha\right)\).