## 5 Case Study: Experimental Results
### Comparison with Topic Models on User Network  
In this subsection, we compare the proposed method with a topic modeling method based on user networks, which is the basic approach that was followed to apply the LDA technique to user analysis in many related studies [24; 28; 29; 30]. Applying the topic modeling technique to user networks is probably  
Figure 6: Active hours and days of the week for two different datasets. Figure 7: Temporal topic flow of PGR21 dataset with \(K=8\) where Topic 2 has significant peaks at certain times. effective for a certain type of data where a large user network, such as the Twitter network, is explicitly established, or in certain cases in which a small number of users are involved for an individual engagement; e.g., only a few authors contribute to a single research paper. However, in online community data, the number of users involved in an individual article is quite large; thus, we would not gain any advantage by constructing the user network over them. Furthermore, aggregating the user co-occurrences over articles would make each of the meaningful engagements indistinguishable. For example, we can suppose such a case in which user A and B have commonly participated in a politics-related article, B and C in a sports-related article, A and C in an art-related article. When we construct the user network here, these three users would form a triangle, which would render these users symmetric and indistinguishable. However, note that our proposed method would be able to distinguish the interests of each user in this case. Figure 8 depicts the histogram of topic distributions of users by comparing the proposed method with the network-based method in which the user network is constructed using co-occurrences. For the purpose of illustration, we ran the topic modeling with two topics, thus each user has a probability distribution \((p,1-p)\); the histograms show the distribution of \(p\) over the users. In the proposed method, users are divided into two groups: those with \(p\approx 0\) and other with \(p\approx 1\), and the other users are almost evenly distributed. This means that users can successfully be clustered using the topic probability. In contrast, network-based topic modeling produced distributions centered at \(p=0.5\). This prevents two topics from being distinguished clearly. For the purpose of quantitative evaluation, we measured the standard deviation of topic distributions as listed in Table 7. Considering a \(M\times K\) matrix, where \(M\) is the number of users and \(K\) is the number of topics, let each row indicate the topic distribution of a user. We computed the standard deviation in both directions: row-wise (user-wise), and column-wise (topic-wise), after which we averaged the values. If the user-wise standard deviation is high, it means a small number of topics form a large portion while the other topics form a small portion; e.g., consider a user with the topic distribution (1,0,0,0). In other words, if this value is low, each topic forms a similar portion, thus they are insignificantly distinguishable; e.g., a user with the topic distribution (0.25,0.25,0.25,0.25) where the standard deviation is zero. On the other hand, the topic-wise standard deviation indicates user variation across a specific topic; e.g., if all users have 0.1 for Topic \(\tau_{1}\), then the standard deviation would be 0 and it means \(\tau_{1}\) is not meaningful for distinguishing users. The proposed method consistently outperforms network-based modeling as the proposed method has higher standard deviations. Figure 8: Topic distributions of users. Users are more clearly distinguished into two groups in the proposed method. The second drawback of applying network-based topic modeling to online community data is that a direct way to obtain article-level results does not exist, despite the use of the proposed article-user topic modeling, where one of the learnt parameters, i.e., the article-topic matrix, explicitly represents the topic distribution of an article.