# Dynamic Community Discovery Method Based on Phylogenetic Planted Partition in Temporal Networks
## 1 Introduction  
### Background  
Complex network analysis is an interdisciplinary research field which can be applied in a lot of areas such as computer science [1; 2] and social, biological and physical sciences [3; 4; 5], and it is capturing the attention of many scholars. A complex network is a simple graph defined as a set of nodes connected by a set of edges. Nodes can represent individuals or organizations. Edges are relational ties between two nodes, e.g., friendship relationships between two social users. Graphs are one of the most important and powerful data structures. Complex network analysis and modeling can be used to reveal patterns of social interaction, to study recommendation systems, or protein complexes and protein functional modules. By far the most basic tasks in complex networks are node identification, link prediction, and information dissemination. These tasks have received extensive research and attention. In addition, community structure discovery is also one of the most important tasks; it is usually defined as identifying tightly connected subgraphs from a complex network. Because communities help to reveal the structure-function relationship of the network, it has been studied extensively. For example, communities within cancer networks mark key pathways associated with cancer progression [6], and the communities in themulti-layer transportation network correspond to common practices, which provides clues for airline management [7]. Therefore, a great deal of work has been carried out in the discovery of communities in the network [8; 9; 10]. A lot of work has been proposed for community discovery, existing algorithms either optimize predefined quantitative functions or acquire potential feature matrices for community detection. Typical methods include modularization-based methods [11], model-based methods [12; 13] and random-walk-based methods [14; 15; 16]. [PERSON] et al. [17; 18] have conducted a comprehensive survey. However, all these methods assume that the target network is static and ignore the timeliness of the network. In reality, many networks from society and nature are dynamic, meaning that the network structure changes over time; that is, it performs the dynamic network. More specifically, in a dynamic network, nodes may appear or disappear over time, and links between two nodes may also appear or disappear. For example, interpersonal relations often change due to individual behavior [19]. For another example, tumor cell migration leads to metastasis, which is crucial for the diagnosis and treatment of tumors [20]. Therefore, it is worthwhile to track how a community evolves in a dynamic network (also known as a dynamic or evolutionary community). For dynamic network modeling, the most widely used method is to introduce explicit smoothing frameworks, which quantifies the similarity between snapshots in two subsequent steps by introducing the Temporal Smoothed Framework (TSF). Various TSF-based algorithms have been proposed to evolve the community by extending the static community discovery algorithm. For example, for topological connectivity, the Kim-Han algorithm [21] found dynamic communities by optimizing modularity, and the DYNMOGA method [22] is presented for the multi-objective genetic algorithm to simultaneously optimize clustering accuracy and clustering drift. Regarding matrix decomposition, the ESPC method [23] is used with matrix spectrum, the ECKF method [24] is proposed by using kernel ENMF, and the Se-NMF method [25] is used by a semi-supervised strategy to develop community testing. The Gr-NMF method [26] is adopted by graph-regularized NMF for community discovery in evolution. In the probabilistic model: FaceNet method [27] is researched by using Maximum a Posteriori (MAP) estimate, DSBM method [28] adopted the Bayesian method to obtain the evolving community by extending the random block model.