## 4 Problem Formulation and Methodology
### Proposed Methodology
#### 4.2.2 Topic Modeling  
Recap the earlier premise, the general idea of a seed-dependent mechanism is to modeled the textual contents based on the given document collection of \(D\), where the \(D\) contained a number of topics, \(T=\{t_{1},\,\ldots\,t_{n}\}\), and each of the \(t\) contained a number of instances \(d\), and defined by a small set of seed words, \(s\). Specifically, the distribution of \(D\) mixture over \(T\) topics, where each of the \(t\) is a mixture of a regular topic (\(\varphi_{t}^{p}\)) and seed topic (\(\varphi_{t}^{s}\)). The model made desirable output during the inference, meaning that \(s\) and other attributes \(a\) that occur in the same context eventually have a high probability in the same topic. In this sense, SLDA inferred the most relevant traits by penetrating the explicit word co-occurrence structures between \(s\) and other regular attributes \(a\) in the \(D\). The model employed the given \(s\) and maximized the relevancy of \(t\) using cooccurrence correlation without employing any predefined labels in training datasets. Thus, SLDA made assumptions that each \(s\) and its corresponded \(t\) associated with a single trait category based on the semantical connotation and word distribution of the training instances in \(D\). The attributes \(a\) and seed words \(s\) were mapped to the dictionary of \(V\) and \(S\), respectively, and all the attributes in \(D\) tokenized at word level and transformed using the Bag-of-Word (BOW) mechanism. In SLDA, the degree of co-occurrence probability between the attributes \(a\) and \(s\) in \(D\) were computed using (2), where \(df(s)\) were the number of instances that contained \(s\) and \(df(a|s)\) were the volume of \(d\) that contained both \(a\) and \(s\). Because our preliminary collected seed words were statistically correlated with PEN model traits [22], it was reasonable to train SLDA to converge and categorize the relevancy between \(d\) and \(t\) via (3) and (4). Equation (3) was applied to determine the relevancy of each attribute to be associated for each \(t\) based on the probability of \(a\) and \(s\) (formula (2)), where the \(S_{t}\) is a set of seed words aggregated to each \(t\). As the conditional probability of \(U(a,t)\) dominated by the statistical properties of \(s\), we determined the maximum value for the attributes by normalizing the weights for \(a\) and rid out the weights of noisy attributes by subtracting the average score and \(\frac{1}{T}\) for each distribution of \(t\) using (4). Based on (4), the higher co-occurrences of \(a\) with \(s\) could resulted larger value of \(U_{n}(a,t)\), where the bigger value indicates \(a\) was more likely to be a salient attribute of \(t\). To simplify, the \(s\) acted as a guide to identify the latent \(a\) using cooccurrence probability to indicate the relevancy of the \(d\) to be categorized under prespecified \(t\). The chance of choosing cooccurrence distribution of an \(a\) aggregated to a trait \(\varphi_{t}\), relies on the domain knowledge supplied by \(S\). However, the nature of the probabilistic model that made the higher-order cooccurrence structures increase the chances of frequent attributes \(a\) co-occurred in the same topic. By considering the weights from (4), we can refine the probability of attribute \(a\) being a feature for topic \(t\) based on (5), i.e., the probability of \(\delta_{a,t}\), that an \(a\) is a latent attribute for a topic \(t\). Although the proposed modeling procedure is similar to the previous nonpersonality study [11], our modeling process used fewer parameters that reduced the computation complexity on exploiting the underlying structure of short texts from SN compared to the existing experiment that used news datasets.