## 5 Case Study: Experimental Results
### User Clustering
#### 5.2.1 Visual Analytics with User Replying Network  
The user replying network (or user interaction network) is a graph representing the intensity of user interactions, where each vertex represents a user, and an edge established between two vertices has a weight, indicating how many times two users exchange comments. It is important to visualize the user replying network, so that we can use visual analytics to determine the characteristics of user interactions and the induced community structure. To visualize this network effectively, we use two graphs: (i) the placement graph, and (ii) the interaction graph. First, we organize the placement graph, in which edge weights are determined by the similarity of the corresponding user vectors of the two end vertices. We set the vertices, each of which indicates a user, and is associated with its topical distribution. We compute the cosine measure for each pair of users as the similarity. For each user, we establish edges to its 10 nearest users with the computed cosine similarities as the weights. Then we perform the force-based layout method on this graph, in order to place the vertices. With this vertex placement, we construct the interaction graph for the final visualization. We label the vertices with their dominant topic, to make the relationship between topics visually clear. Then we remove all the edges computed by the topical similarity among users. We reestablish edges using the user replying network, which completes the user interaction graph. The weight of an edge between users is set to the number of articles in which the two users wrote comments to each other. We visualized the constructed graph using Gephi [38]. Figures 4 and 5 show the visualized user replying networks obtained using the user-topic model. Vertices are placed according to the dominant topic of the corresponding users. The dominant topics of different users are indicated using different colors. As described, the thickness of an edge indicates weight, which measures how many times the two users interacted. We also assigned different sizes to vertices to represent their degrees (the numbers of neighbors in terms of user interaction). We see individual characteristics in these visualizations. Comparing the two Reddit datasets depicted in Figure 4, we observe that users with different topics in \(r\)/politics are separated more clearly than those in \(r\)/AskReddit. There are more thick edges observed in \(r\)/politics, which indicates two users meet and debate in many articles, while two users in \(r\)/AskReddit rarely meet each other again. This low probability is due to the excessively large numbers of users and articles. Long-tailed user groups are observed in both Reddit datasets, on the right sides of the figures. If there are a number of users with the same topic whose nearest neighbors are similar to them, edges are unlikely to be connected outside this topic group. This leads to a protrusion (\"long tail\") during the force-based vertex placement, and indicates that some users in this topic have generally participated only in some particular articles. In \(r\)/politics, they may be avid supporters or critics of a certain political group, although we should investigate more closely to discover the cause of this phenomenon. In \(r\)/AskReddit, articles include questions targeting specific groups of people such as transgender people, girls wearing long claw-like nails, and people with face tattoos. These articles also include questions asking users for their personal tips, experiences or preferences, that others do not have. Perhaps these target-specific questions cause the users who participate in these articles to group together tightly. We also observe that users with related thematic topics are placed close together. Recall that we place the user vertices according to the similarity of their topical distribution vectors. Thus, users close to each other on the graph are likely to share behavioral characteristics.