# Edge-Nodes Representation Neural Machine for Link Prediction
## 2 Related Work  
In the past few decades, link prediction has drawn lots of researchers' attention. Many useful methods have been proposed for link prediction task, which can be divided into three categories: topological feature-based, latent feature-based and link embedding-based. The details are explained in the following. Topological feature-based method extracts the features hidden inside the nodes and edges' structures. A heuristic score is used to measure the similarity and connectivity between two nodes. Many heuristic methods perform very well on improving the accuracy of link prediction. Common  
Figure 2: The ENRNM framework, the green strips indicate the edges’ representations generated from the subgraphs and the yellow strips indicate the nodes’ representations. For each target link, we combine the edge and two nodes’ representations as link’s representation namely formation mechanism. A neural network is used to predict whether the link exists. neighbors (CN) [1] predicts link's existence by the amounts of common neighbors of two nodes. [PERSON] [21] considers that a link may exist when the common neighbors account for a high percentage of all neighbors of two nodes. [PERSON] (AA) [4] assumes that the common neighbors play an important role in a link's formation if the neighbors' number of these common neighbors is small. Besides, there are many other popular heuristic methods as shown in Table 1, empirical comparisons of these heuristics on different networks can be found in [22]. Latent feature-based method tends to get the representations and properties of nodes, which are often obtained in the way of factorizing a matrix [23] such as the adjacency matrix or the Laplacian matrix. Through factorizing a matrix, we can get the representation of each node in the form of a low-dimension vector. Then we can conduct the link prediction task by combining two nodes' low-dimension vectors as link's representation for each link. Latent feature-based methods focus on the individual nodes and miss the structural similarities between nodes, high-dimension vectors are needed if we want to utilize the heuristic information. Link embedding-based method is an emerging approach, it learns a link's formation mechanism from the network by itself other than assuming a particular mechanism (such as common neighbors). A typical method is WLNM [16] which extracts an enclosing subgraph for each link and encodes the subgraph to an adjacency matrix as link's surrounding environment, namely the link's representation. A neural network is trained to predict the link's existence. The method is universal for the reason that it works well on almost all kinds of networks, and it outperforms many other methods. Another method SEAL [24] also performs pretty well on all kinds of networks. SEAL learns link's formation mechanism from subgraph, node embedding, attributes and trains a graph neural network(GNN) for link prediction. Another link embedding-based method does not acquire link embedding directly but represents the link by combining the two nodes' representations on the two sides of the edge in different manners. Network embedding has been a hot topic recently because of the pioneering work DeepWalk [17]. DeepWalk uses random walks beginning from a node as a node sentence which is similar to a word sentence, then it trains a skip-gram model [25] to learn the node embedding of a specific network. Different from word embedding whose input is a significant corpus and output is almost all the words' embeddings, network embedding method needs to learn node's embedding for each network since these networks are isolated from each other. On the basis of the DeepWalk, Node2 vec [18] and