## 5 Results
### Effectiveness and Efficiency Evaluation of the Model
For each query node, we first calculate the fitness of the queried community and then count the proportion of communities in different fitness intervals. As shown in Figure 4a, the fitnesses of 83% of TWC communities vary in the range of 0.5-0.7, while the fitnesses of 70% of TWOD communities are in the range of 0.4-0.5. Only when two users check in the same project will the TWOD model think that the two users are similar; otherwise, the corresponding value in the user-user matrix is 0. However, friends may just check in for similar items, which leads to the user-user matrix failing to capture the real social relationship. Hence, the community's fitness based on the user-user matrix is not high. TWC model is based on the social network snapshot, which reflects the real social relationship between users. In addition, the similarity between users is evaluated according to the historical occupancy records of users so that the community can be better divided. Since TWOD is not affected by \(k\), we evaluate the change in the median fitness of the community queried by the TWC model at different k. As shown in Figure 4b, the community's fitness increases with the growth of k and finally tends to be stable. Compared with \(k=10\), the fitness of the TWC model is better than that of TWOD. * Experiment 3: the effect of k on effectiveness Since TWOD is a global community detection, we will not compare it with other community search models. We gradually vary parameter \(k\) from 8 to 20 and compare the improvement of \(H_{\textit{func}}\) in similarity score compared with \(H_{\textit{func}}\). As shown in Figure 5a, no matter the value of \(k\), the community score of \(H_{\textit{func}}\) is better than that of \(H_{\textit{func}}\). This is because the scoring function of TWC defines the decisive role of query nodes and selects nodes with high similarity in descending order, while the scoring function of VAC measures the similarity between all nodes, which undoubtedly weakens the leading role of query nodes. As \(k\) grows, the improvement tends to be stable. This is because the initial feasible community is smaller and more stable. The lowest similarity score determines the community score, and so the average similarity of the community also has the same trend. Figure 4: Community fitness comparison. (**a**) Proportion of communities in different fitness ranges when \(k=10\); (**b**) median of community fitness with different \(k\). Experiment 4: the effect of query time window on effectiveness. Let us set the whole record time of the dataset as a time window and the latest timestamp as the start of the window. In reverse order of time, five sub-windows are set, denoted as 20%, 40%, 60%, 80%, and 100% time windows, respectively. Then, we compare the improvement of \(H_{\text{frac}}\) in similarity score compared with \(H_{\text{frac}}\). As shown in Figure 5b, the improvement is not obvious when the time window is small. This is because the check-in records included are relatively few and fresh, so the difference in weights is not obvious. As the time window enlarges, more and more records are included in the calculation. The difference between attribute weights is gradually enlarged, which is more conducive to filtering out low-weight attributes. Hence, the score improvement is more obvious. However, the improvement is reduced when the time window is large enough, indicating that blindly expanding it is not appropriate because it will include the old and frequently occurring attributes in the user's interest list and disperse the weight of these significant attributes. * Experiment 5: the effect of \(k\) on efficiency. Since the efficiency of the TWC model is only affected by \(k\), and the communities found by the Local Extend algorithm and the Shrink algorithm are the same, we vary \(k\) to compare the efficiency of different modes. As shown in Figure 6, the community is large and incohesive enough when \(k\) is small.