# Dynamic Community Discovery Method Based on Phylogenetic Planted Partition in Temporal Networks
## 4 Results
### Synthetic Networks  
The artificial network is generated in this paper, which consists of 128 nodes, initially divided into four communities, where each community has 32 nodes. At the initial time step, the edge probability of the system evolution migration partition is set as \(\varepsilon_{pp}^{1}=0.3109\) and \(\varepsilon_{pq}^{1}=0.0765\) (\(p,q=1,2,3,4\) and \(p\
eq q\)). The initial covariance \(\Theta^{1}\) is set to the identity  
Figure 4: The simulation of the evolution process of an artificial dynamic network. matrix 0.04\(I\). The state vector \(G\) evolves according to the Gaussian random walk model, namely \(H^{t}=I\) in Equation (15). This paper generates 25 and 50 time steps. At each time step, nodes are randomly selected to leave their communities and randomly assigned to one of the other three communities. Table 2 statistically compares the proposed PPPM method with the average _ARI_ experimental results of multiple parameters of four representative models in an artificial network environment. In Table 2, bold font indicates that the result is the best. It can be clearly seen that the proposed PPPM method has the best performance under all parameters. It can be calculated that the average performance of the novel method is improved by 0.05 compared with the other four best models. Figure 5 shows the comparison of average ARI results between the proposed method and four representative models in an artificial network environment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time Step** & **Random Rate** & **Proposed PPPM** & **PisCES** & **CLBM** & **SBM + MLE** & **FaceNet** \\ \hline
25 & 10\% & **0.65702** & 0.50409 & 0.48838 & 0.56099 & 0.46667 \\
50 & & **0.56630** & 0.38265 & 0.34544 & 0.49414 & 0.34324 \\
25 & & **0.72236** & 0.57972 & 0.54694 & 0.66961 & 0.50949 \\
50 & 20\% & **0.94401** & 0.90616 & 0.89504 & 0.92753 & 0.88592 \\ Mean & & **0.72242** & 0.670 & 0.56895 & 0.663068 & 0.55133 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of the proposed PPPM and representative model on the Mean ARI (synthetic data). Figure 5: Comparison of the proposed model with 4 different models on Mean ARI (synthetic network). (**a**) indicates that the time step is 25 and the randomly selected parameter is 10%, (**b**) indicates that the time step is 50 and the randomly selected parameter is 10%, (**c**) indicates that the time step is 25 and the randomly selected parameter is 20%, (**d**) indicates that the time step is 50 and the randomly selected parameter is 20%. As shown in Figure 5a, 25 time steps are generated by the artificial network. On each time step, the randomly selected parameter is set to 10%. In this experiment, the parameters of the noise item are changed at the 15 th time step (the left line) and set back to the original state at the 16 th time step (the right line). It is evident that in the 15 th time step, the only two models with SBM and PPPM + MLE line charts show the correct change in trend, i.e., a downward trend, and the proposed PPPM method declines faster, and the increasing trend of PisPCES, CLBM, and FaceNet are unaffected and keep the previous state, after the 16 th time step, which also can obviously show that compared with the other four kinds of models, the novel method callback trend is more obvious. This indicates that the proposed novel method has a more consistent response to noise terms. In Figure 5b, the artificial network generates 50 time steps, randomly selects parameters and sets them to 10%, changes the parameters of the noise item at the 20 th time step (the left line), and sets them back to the original state at the 21 st time step (the right line).