## 3 Materials and Methods
### Evaluation Method  
To evaluate the performance of the BTM topic model in the ASA-UXF framework, an optimized semantic coherence score was introduced by [PERSON], [PERSON], and [PERSON] et al. [52] to assess the quality of the extracted topics. This evaluation metric as shown in Equation (4) is characterized by being well aligned with assessments of human coherence, and it does not rely on an external reference corpus; rather, it solely uses word co-occurrence data obtained from the corpus being modeled. Ideally, the model would already have taken into consideration all of these co-occurrence data. To assess a topic set's overall quality, we computed its average coherence score, which is calculated using Equation (5):  
\[C(z;V^{(z)})=\sum_{t=2}^{T}\sum_{l=1}^{t}\log\frac{D(V_{t}^{(z)},V_{l}^{(z)})+1 }{D(V_{l}^{(z)})} \tag{4}\]  
\[\frac{1}{K}\sum_{k}C(Z_{k};V^{(Z_{k})}) \tag{5}\]  
where \(z\) is the topic, \(T\) represents the top words \(V^{(z)}\), \(D(v)\) is the document frequency of word \(v\), \(D(v,v^{\prime})\) is the co-document word frequency \(v\) and \(v^{\prime}\), and \(K\) is the number of topics.  
Perplexity is a popular evaluation metric in topic models that is used to assess the model's ability to anticipate new documents. It refers to the model's uncertainty in predicting the next word for a given batch of documents. Further, with decreasing perplexity, the model's ability to forecast new documents increases. In general, models with lower degrees of perplexity perform better in predicting the next word [53]. To calculate the perplexity of the unseen comments for the testing dataset, Equation (6) was applied:  
\[\text{Perplexity}=\exp\,(-\frac{\sum_{d=1}^{m}\log p(w_{d})}{\sum_{d=1}^{m}N_ {d}}) \tag{6}\]  
where \(w\) is a collection of comments, \(m\) is the total number of comments, \(p(w_{d})\) is the likelihood of a word appearing in a comment, and \(N_{d}\) is the word count of the comment.  
The silhouette score is a popular and common metric used to assess the quality of data clustering outcomes such as k-means. This score depends on distance metrics such as \"Manhattan\", \"cosine similarity\" or \"Euclidean\" to assess the similarity of each data point to the assigned cluster and how it is different from other clusters. In detail, a positive score indicates good clustering results, a score of zero indicates overlapping clusters, and a negative score indicates poor clustering results [54]. Equation (7) was used to evaluate clustering performance:  
\[\text{silhouette score}=(b-a)/\max(a,b) \tag{7}\]where for every data point, \(b\) is the mean nearest-cluster distance, and \(a\) is the mean intra-cluster distance.  
The Euclidean distance metric is a commonly used distance measure. It is based on the Pythagorean theorem and represents the shortest distance between two data points. Many machine learning methods employ the Euclidean distance as the default distance metric to compare the similarity of two recorded vectors [55]. It can be calculated using Equation (8):  
\[D=(\sum_{i=1}^{n}(x_{i}-y_{i})^{2})^{\frac{1}{2}} \tag{8}\]  
where \(n\) is the number of dimensions, \(x_{i}-y_{i}\) represent the data points, and \(D\) represents the distance between these data points.  
The cosine similarity metric is a method for measuring the similarity of two vectors (two reviews) by computing the cosine of their angle [56; 57]. To compute the cosine similarity between two vectors, \(A\) and \(B\), Equation (9) was used:  
\[cos\_sim(A,B)=cos(\theta)=\frac{\sum_{i=1}^{n}A_{i}B_{i}}{\sqrt{\sum_{i=1}^{n} A_{i}^{2}}\sqrt{\sum_{i=1}^{n}B_{i}^{2}}} \tag{9}\]  
where \(\theta\) represents the angle between \(A\) and \(B\) in the n-dimensional space, and \(A_{i}\) and \(B_{i}\) are the \(i^{th}\) components of reviews \(A\) and \(B\), respectively.