# Dynamic Community Discovery Method Based on Phylogenetic Planted Partition in Temporal Networks
## 2 Related Work  
According to the research of [PERSON] et al. [32], the dynamic community discovery algorithms can be divided into four categories: coupling network, two-stage algorithm, evolutionary clustering, and probability model. However, [PERSON] et al. [33] believed that all existing dynamic community discovery methods can be identified as online or offline methods. [PERSON] and [PERSON] [31] proposed a new survey on community detection in dynamic networks, which proposed the unique functions and challenges of dynamic community discovery algorithms. The first kind of coupled network-based algorithm firstly builds the network by fusing edges at different times. Then, the classical static community detection algorithm is used to find the communities in the coupled network. For example, [PERSON] et al. [34] discovered the ongoing events in the microblog message flow by adding edges between vertex instances at different times to build the coupling network, in which the dynamic community corresponds to the community in the built network. Because coupled networks cannot fully describe the dynamic characteristics of networks, these algorithms have been shown to accurately discover only short-cycle communities. To overcome this problem, the second kind of two-stage algorithm separated the community detection from the community dynamic, avoiding the coupling of the dynamic network. Specifically, these algorithms used static community detection algorithms to find the community each time and then connected the community the next two times to extract the evolving community. Typical algorithms included GraphScope [35] and TRMMC [36] coupled networks and two-stage algorithms that detected dynamic communities in a dynamic network by simply extending static community detection methods and detecting dynamic communities in each operation dynamic network or static community. In general, these algorithms can achieve better performance in the case of weak network dynamics. In this case, the dynamic update method can accurately identify the dynamic community without running the community detection algorithm each time, and only need to update the previously discovered community. However, the accuracy of these algorithms is low. The third type of dynamic community discovery method is related to clustering evolutionary, which is proposed by [PERSON] et al. [37]. They extracted the implicit community structure in each snapshot, which is one of the most widely used methods for dynamic community discovery. The evolutionary clustering algorithm adopted the assumption of time smoothness. The community structure will not change much over a continuous-time slice. This time smoothing method can be used to overcome the randomness. Compared with other algorithms, the evolutionary community discovery algorithm aims to discover a smooth sequence of communities in a series of network snapshots (as can be seen in Figure 2). The overall objective function of the evolutionary algorithm can be decomposed into two parts: Snapshot Cost (CS) and Temporal Cost (CT) [38]. \[Cost=\alpha\cdot CS+(1-\alpha)\cdot CT \tag{1}\]  
Among them, \(CS\) measures the adaptability of the community structure and network at the time \(t\), while \(CT\) measures how similar the two community structures (the community structure is acquired at the time \(t\) to the structure is obtained at previous time \(t-1\)). The parameter \(\alpha\) is for balancing the importance between \(CS\) and \(CT\). By introducing different object functions based on modularity, normalization of mutual information and spectrum clustering et al., this framework has been used in much of the literature [39; 40] to discover communities in dynamic networks. [PERSON] and [PERSON] [39] formalized the dynamic community discovery algorithm as a multi-objective optimization problem, which maximized the clustering accuracy of the  
Figure 2: The series of network snapshots. current time step and minimized the clustering drift from one time step to one successive time step.