## 4 Experimental Results and Comparative Analyses
### Datasets and Experimental Setup
#### 4.1.2 Evaluation Metric  
As the number of topics produced by a dynamic topic model does not adequately gauge its quality or superiority compared to other models, we assessed the performance of the topic models from the perspectives of human interpretability and diversity. Specifically,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pagent Subjects** & **Periods** & **Documents** & **Vocabulary** & **Tokens** \\ \hline NSTs & 2016–2024 & 22,834 & 18,945 & 16.952 MB \\ RISs & 2016–2024 & 7863 & 9705 & 6.070 MB \\ ISAC & 2016–2024 & 14,918 & 21,715 & 15.055 MB \\ ISAGSC & 2016–2024 & 17,240 & 14,918 & 12.462 MB \\ EAIs & 2016–2024 & 15,770 & 17,876 & 11.386 MB \\ \hline \hline \end{tabular}
\end{table}
Table 1: The statistics of 6G patent datasets used in the experiment.  
we adopted two widely used metrics, namely, topic coherence and topic diversity, for this evaluation.  
Topic coherence (TC) [58], referring to the coherence of top words in a topic, indicates the interpretability of a topic containing \(m\) words. If the words in a topic often appear together in the same documents, it indicates that the topic has a high coherence. We employed the popular the co-occurrence metric CV as the coherence metric [59], which outperforms early metrics like Normalized Pointwise Mutual Information (NPMI) [60], which is an improved version of \(PMI\)[61]. The formula for \(PMI\) is as follows:  
\[PMI\big{(}w_{i},w_{j}\big{)}=log\frac{P\big{(}w_{i},w_{j}\big{)}}{P\big{(}w_{i} \big{)}P\big{(}w_{j}\big{)}} \tag{3}\]  
where \(P(w_{i})\) and \(P\big{(}w_{j}\big{)}\) are the probabilities of words \(w_{i}\) and \(w_{j}\) being present in the window, and \(P\big{(}w_{i},w_{j}\big{)}\) is the probability that both are present in the window. \(NPMI\) normalizes \(PMI\) to keep the values between \(-1\) and \(1\), potentiating the result for better differentiation. Its formula is:  
\[NPMI(w_{i},w_{j})^{\gamma}=(\frac{PMI\big{(}w_{i},w_{j}\big{)}}{-log\big{(}P \big{(}w_{i},w_{j}\big{)}\big{)}})^{\gamma} \tag{4}\]  
The context vector for a word \(w_{i}\) is then  
\[\overset{\rightarrow}{v}(w_{i})=\left\{\sum_{w_{j}\in W}NPMI(w_{i},w_{j})^{ \gamma}\right\} \tag{5}\]  
where \(W\) is the vocabulary. For a given topic, the cosine similarity between the context vectors of all its top words was calculated. After that, all these distances were aggregated, and the average value is the topic coherence \(Cv\). To measure the association between a topic and its time slice, we also used the documents within that time slice as a reference corpus to estimate the probabilities of word occurrences. In practice, a higher TC value implies that the topic exhibits greater coherence within the documents of the time slice.  
_Topic diversity_ (\(TD\)) [62] is used to evaluate the degree of difference in representing a given set of topics. For a given topic within a specific time slice, we calculated the proportion of its 15 top-ranked words that both occur only once and are present within that same time slice. \(TD\) is defined as the percentage of unique words in the top \(N\) words of the topics. The formula for \(TD\) is relatively straightforward:  
\[TD=\frac{\text{Number of unique words in top $N$ words}}{\text{Total number of top $N$ words}} \tag{6}\]  
\(TD\) is used to evaluate the distinctiveness of topics. A \(TD\) value close to 0 suggests many repeated words among the topics, indicating redundant topics. On the other hand, a value close to 1 implies that the topics are more singular, with a high proportion of unique words. In a news article corpus, high \(TD\) values would mean that different topics cover a wide range of distinct concepts, while low \(TD\) values might indicate that topics are overlapping and less diverse. Consequently, \(TD\) can be used to determine whether repetitive topics exist. This metric is useful for ensuring that the topics generated by a topic model are diverse enough to represent different aspects of the corpus content.