# Dynamic Community Detection Based on Evolutionary DeepWalk
## 2 Related Work
### Community Detection  
The community detection method based on graph embedding usually embeds the network into the low-dimensional space first, then uses a clustering algorithm, such as K-Means, to classify the embedding results and classifies the community types.  
In the static community detection methods, some studies have tried to use graph embedding methods. [PERSON] et al. [20] proposed the concept of community embedding and studied the distribution of community structure in low-dimensional space. They think that community detection, node embedding, and community embedding form a closed loop. According to the closed-loop theory, they combined the three methods to establish a community embedding framework. The CommunityGAN [21] framework focuses on the clique structure in the network and applies a generative adversary network theory to community detection for the first time. In the generator, CommunityGAN uses positive sampling for clique distribution and negative sampling for the whole graph structure. However, the above two methods need to know the number of social network communities, which is precisely the condition that most real-world networks cannot have.  
At present, most of the graph embedding methods are only applied to static community detection, while the research on dynamic community detection is less. According to different research frameworks, dynamic community detection methods can be divided into evolutionary graph clustering-based methods and incremental clustering-based methods.  
The evolutionary graph clustering method mainly uses the idea of evolutionary clustering. It considers that the network evolution has temporal smoothness. In the process of the network development with time, only a few nodes and edges change, and the overall structure of the network will not change. In real life, the real network evolution basically conforms to this situation. Our method is also based on this premise. Evolutionary clustering was first proposed by [PERSON] et al. [22] in 2006. It uses temporal smoothness to balance the communities obtained in two continuous-temporal snapshot networks. It consists of snapshot cost (CS) and temporal cost (CT), where CS represents the degree of community structure in the current temporal snapshots, and CT is a measure of how similar the community structure of the current temporal snapshot network is to the community structure of the previous temporal snapshot. The cost function is represented by the following Equation (1):  
\[\text{Cost}=\alpha\text{CS}+(1\text{-}\alpha)\text{CT} \tag{1}\]  
The FacetNet [23] is inspired by the idea of evolutionary clustering. It combines the historical community structure with the current community to detect the community and uses non-negative matrix decomposition as an expression to unify the formal community. [PERSON] et al. [24] proposed a graph regularized evolutionary nonnegative matrix factorization algorithm for dynamic community detection based on the idea of evolutionary graph clustering. To balance temporal cost and snapshot cost, the algorithm using regularization exam is used to optimize the temporal cost of the overall objective function.  
The incremental clustering method mainly deals with changing elements from the behavior patterns of nodes and edges. When nodes and edges in the network are added or deleted, the dynamic community detection algorithm will judge and classify the changed elements. Dyperm [25] is an incremental community detection that takes permanence as the attribute of incremental elements. It discriminates the changing elements and their associated changing elements in each scenario to discover the changing elements in the temporal snapshot network.