# MSGCN: Multi-Subgraph Based Heterogeneous Graph Convolution Network Embedding
## 1 Introduction  
In recent years, network embedding [1, 2] (also called network representation learning) has attracted wide attention due to its widespread application in practical scenarios, such as social networks, protein interaction networks, citation networks, and so on. Network embedding aims to map the latent intrinsic feature of node, link, or the whole network into a low-dimensional space so as to enhance the performance of downstream machine learning tasks, such as node classification, node clustering, and link prediction. The low-dimensional vector representation obtained from network embedding can retain the original network information in many aspects, such as network structure information and node feature information, to make the embedding capability better. To this end, scholars have proposed many models. The classical models include DeepWalk [3], Node2 vec [4], LINE [5], GraphSAGE [6], GCN [7], and GAT [8], which give great inspiration to later researchers. However, most of these methods are used for homogeneous graphs and do not take the types of nodes and edges into consideration. However, a heterogeneous graph [9, 10] composed of multiple types of nodes and edges is also very common [11]. Some methods for heterogeneous graphs have been proposed, such as HAN [12], HERc [13], HetGNN [14], HGT [15], HIN2 Vec [16], HGSL [17], and HeCo [18]. Most of the existing methods including the latest methods are based on metapaths. Although these types of methods are good at retaining semantic and network structure information, there are also some drawbacks. Firstly, the design of the metapathrelies on domain knowledge, and different metapaths lead to different node embeddings. Secondly, these metapath-based methods rarely use the content information, but the latest models hardly have this problem. Thirdly, most of the previous methods are transductive learning methods, and very few are inductive learning methods. When a new node appears, the model has to be retrained on the entire dataset in order to get the representation of the new node, which is computationally expensive. Actually, we can design a heterogeneous graph embedding method without using metapaths. At the same time, the model can also cope with the inductive learning tasks. In order to address the above problems, we think the core problem of heterogeneous graph processing is how to transform the structure between different types of nodes and edges into the common space so that the structure and semantic characteristics of the heterogeneous graph can be encoded. In order to address the above problems, this paper proposes a new model to deal with heterogeneous graphs, called MSGCN (Multi-Subgraph based Graph Convolution Network). The model consists of three components: original graph decomposition, subgraph convolution, and aggregating node representations. In the first component, we preprocess each dataset to ensure the content information of each node has the same dimension, so that we can decompose the original graph into multiple subgraphs [19; 20] according to the type of edges. In the second component, we apply convolution operation on each subgraph to obtain the node representations. In the third component, we aggregate each above node representations to get the final node representations. We further consider the application of the model, so we have the module of the inductive learning task. In this module, a new node sampling method is proposed to generate node representations of unseen nodes quickly without retraining the whole dataset, which fully considers the importance of each node in the network. In summary, the contributions of this paper are as follows:  
* A new method is proposed to deal with different types of edges to solve the heterogeneity of edge types. None of the previous approaches attempted to decompose the original graph into multiple subgraphs by type of edges. The subgraphs after decomposition can be viewed as homogeneous graphs, and they can be further processed using the methods previously applied to homogeneous graphs.