# Visual Analytic Method for Students' Association via Modularity Optimization
## 8 Experimental Results
### Discovering Communities via Louvain Algorithm  
To illustrate the process of discovering student communities via the Louvain algorithm, we carried out five iterative operations; the results are shown in Table 3. After the first iteration operation, there are 1083 communities, the number of people in the largest community is 630, and the number in the smallest is 1. With increasing iteration operations, the number of communities decreases and the number of people in the largest community increases. After the fifth iteration, the gain of modularity approximately approaches zero, indicating that the algorithm has reached a stable state. We further combine the basic information of students, such as grade and class information, to analyze the discovery results, and conclude that students with lower grades tend to form large communities and those with higher grades tend to form small communities. This is consistent with common sense.  
In addition, to manually verify the experiment, we constructed an association network of 88 students from a designated major, and discover the community structure via Algorithm 1. After two iterations, the iterative operation converged and the community structure stabilized at nine communities, as shown in Table 4. Students belonging to the same community should have similar spatiotemporal patterns. The no. 1 community consists of two students 150301 ci and 150301 dg, who live in the same room and often have meals and attend classes together, and the similarity value between them is 0.82. The no. 2 community has 42 members belonging to the same class. By communicating with the counselor, we found that the performance of this class is excellent. The 11 students in community no. 3 often play games and have meals together. The no. 4 community also has two members, 150301 ab and 150301 bd, who are lovers, and the similarity value is 0.63; they often have meals and participate in campus activities together. The no. 5 community also contains two students, 150302 cj and 150241 de, with a similarity value of 0.78, and while they have different majors, they are very familiar with each other and often do things together. The 14 students in no. 6 community are from same major, with similarity value 0.83, they belong to a learning team and hold regular study activities in library twice one week. The no. 7 community is the same as the no. 8 community, they have two girl students who are in a close friendship. The no. 9 community has 11 students who are from different majors, with a similarity value of 0.69, these students belongs to one basketball team, they often shower and have meals together after training. Through these offline verifications, we showed that the Louvain algorithm can effectively discover the associations among students based on their activity sequences.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Student ID** & **FeaSim** & **SpaSim** & **SpaTemSim** & **Spa\_SpaTemSim** & **Spa\_FeaSim** & **SpaTem\_FeaSim** \\ \hline
151441 af & 0.45 & 0.69 & 0.78 & 0.66 & 0.67 & 0.64 \\
151441 ag & 0.45 & 0.69 & 0.89 & 0.66 & 0.67 & 0.64 \\
151441 ah & 0.12 & 0.86 & 0.95 & 0.79 & 0.79 & 0.71 \\
151441 ai & 0.33 & 0.85 & 0.94 & 0.66 & 0.8 & 0.75 \\
151441 ba & 0.33 & 0.85 & 0.93 & 0.66 & 0.8 & 0.75 \\
151441 bd & 0.41 & 0.73 & 0.92 & 0.6 & 0.7 & 0.67 \\
151441 bc & 0.41 & 0.73 & 0.9 & 0.6 & 0.7 & 0.67 \\
151441 bf & 0.37 & 0.94 & 0.92 & 0.6 & 0.88 & 0.82 \\
160415 gj & 0.37 & 0.94 & 0.79 & 0.6 & 0.88 & 0.82 \\
160416 aa & 0.26 & 0.86 & 0.83 & 0.64 & 0.8 & 0.74 \\
160416 ab & 0.26 & 0.86 & 0.86 & 0.64 & 0.8 & 0.74 \\
160416 ae & 0.32 & 0.73 & 0.91 & 0.6 & 0.69 & 0.65 \\
160416 ad & 0.32 & 0.73 & 0.91 & 0.6 & 0.69 & 0.65 \\
160416 ag & 0.29 & 0.9 & 0.91 & 0.59 & 0.84 & 0.78 \\
160416 ah & 0.2 & 0.72 & 0.91 & 0.62 & 0.67 & 0.62 \\.. &.. &.. &.. &.. &.. &.. \\ \hline Average Ratio & 0.32 & 0.78 & 0.87 & 0.67 & 0.73 & 0.71 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accuracy computed via six similarity operators.