# Multi-Layer Feature Fusion-Based Community Evolution Prediction
## 3 Multi-Layer Feature Fusion-Based Community Evolution Prediction
### Community Mesoscopic Feature Mining  
This section will first introduce the definition of community mesoscopic features proposed in this paper. Then, this section will propose the corresponding mesoscopic feature-mining algorithm based on the community hypergraph. Figure 1: Calculate degree from global scope and local scope. Community is a mesoscopic structure in the network. In the real world, there is much interaction between communities. These interactions will also have an impact on the future evolution of the community. To consider the influence relationship between communities, we define the community mesoscopic feature, which is defined as follows:  
**Definition 3** (Community mesoscopic feature). : _Community mesoscopic feature describes the mutual influence relationship between communities. It is a concrete manifestation of the influence of other communities on this community. In this paper, the community mesoscopic feature of community C is represented by \(F_{C}\). The mesoscopic features of all communities are represented by matrix F._  
Since the interaction between communities is a complex and abstract effect, the mesoscopic features of the community cannot be obtained through simple calculation. To accurately discover the community mesoscopic features, we propose an algorithm for mining mesoscopic features. This algorithm first treats the community as a hypernode in the network, then constructs a community hypergraph based on the similarity between hypernodes. Finally, the algorithm obtains the community mesoscopic features through NMF. We first give the definition of the community hypergraph, as follows:  
**Definition 4** (Community hypergraph). : _Hypergraph is a concept opposite to the simple graph. A node in a hypergraph is a set of nodes, and the edges in a hypergraph describe the relationship between the set of nodes. A community hypergraph is a hypergraph constructed by treating a community as a node. We refer to the community in the hypergraph as community hyper-nodes._  
Figure 2 shows an example of a community hypergraph. In Figure 2, the network on the left is the original network, in which the nodes of the same color belong to the same community. The network on the right is the community hypergraph constructed from the original network, and the relationship between the hypernode and the community is given by the solid arrow. As can be seen from Figure 2, by constructing the community hypergraph, the algorithm can ignore the complexity of the internal connections of the community, and it can focus on mining the influence relationship between the communities. In addition, in the original network, there is no direct connection between the blue community and the green community. But in the hypergraph, the blue node and the green node are connected, because in the real network, the influence between the community can be generated not only through the interconnection of nodes between communities, but also through other means, such as mutual attention between communities and so on. Figure 2: The example of hypergraph. In this paper, the community hypergraph is constructed by calculating the similarity of community hyper-nodes. The weight of the edges in the hypergraph is the corresponding hypernode similarity. The definition of hypernode similarity is as follows:  
**Definition 5** (Hypernode similarity). : _Hypernode similarity describes the degree of similarity between community hyper-nodes.