# Hypernetwork Representation Learning with the Set Constraint
## 2 Related Works  
Network representation learning aims to learn a low-dimensional vector for each node in the network, preserving the structure and inherent characteristics of the network. More and more researchers have focused on network representation learning in recent years. For example, Deepwalk [4] introduces Skip-Gram [22], a widely-used distributed word representation method, into the study of the network to learn node representation vectors. node2 vec [5] maximally preserves the network neighborhoods of the nodes through a biased random walk strategy, and maps the network nodes to a low-dimensional feature representation space. LINE [6], which can be easily extended to a network of millions of nodes and billions of edges, carefully designs an objective function that preserves both first-order and second-order proximities. SDNE [7] captures highly nonlinear network structures and utilizes first-order and second-order proximities to characterize local and global network structures. HARP [8] is proposed to learn low-dimensional representations of a graph's nodes to preserve high-order structural features by compressing the input graph prior to graph embedding. However, the above-mentioned network representation learning methods only utilize the network structure to learn the node representation vectors, and do not consider heterogeneous information associated with the nodes, such as text, community or label information of the nodes. To cope with this issue, researchers have incorporated heterogeneous information associated with the nodes into the topology-based network representation learning methods. For example, CANE [9] learns the context-aware representation vectors of the nodes with mutual attention mechanism, and models semantic relations between the nodes. CNRL [10] utilizes the similarities between the text theme and the network community to incorporate community information, a key network analysis factor, into the process of network representation learning, which simultaneously detects the community distribution of each node and learns the representation vectors of the nodes and the communities. PPNE [11] effectively incorporates the network topology and attribute information of the nodes into the process of network representation learning. Nevertheless, the network representation learning methods listed here only consider the pairwise relationships between the nodes in the traditional network. However, in the real world, the complex interaction relationships among no less than two nodes need to be considered sometimes, and the complex relationships can be modeled by the hypernetwork. Unfortunately, the above network representation learning methods are not appropriate for the hypernetwork, since these methods do not fully consider the hypernetwork topology structure. So far, only a few hypernetwork representation learning methods have been proposed. For example, [PERSON] [14] extends the powerful method of spectral clustering that is originally run on undirected graphs to the hypergraph, and further develops the hypergraph embedding algorithm on the basis of the spectral hypergraph clustering method. [PERSON] [15] extends the traditional spectral hashing to the hypergraph and accelerates the similarity search of social images by mapping semantically related nodes to similar binary codes within a short hamming distance. [PERSON] [16] utilizes two hypergraph views to represent text-related and theme-related images and proposes a spectral multi-hypergraph clustering algorithm to classify the images. HGNN [19] a hypergraph neural network model for data representation learning. HPHG [20] proposes a deep model named as hyper-gram to learn low-dimensional representation vectors. DHNE [21] is proposed to learn low-dimensional representation vectors of the hypernetwork with non-decomposable hyperedges. HHNE [23] is a depth model based on graph convolutional network, which incorporates the features of the nodes into the process of network representation learning.