# Hypernetwork Representation Learning with the Set Constraint
## 1 Introduction  
Networks are ubiquitous in our daily life, and many real-life applications focus on mining valuable information from networks. A basic issue of data mining is how to learn ideal node representation vectors. To cope with this issue, network representation learning has been proposed to learn a low-dimensional representation vector for each node in the network, which can be applied to lots of machine learning tasks such as node classification [1], link prediction [2], and community detection [3]. Most of the related works learn node representation vectors only from the network topology structure, such as Deepwalk [4], node2 vec [5], LINE [6], SDNE [7], and HARP [8]. The basic assumption of these topology-based representation learning methods is that the nodes with similar topological contexts should be tightly distributed in the low-dimensional vector representation space. However, in many real scenarios, the vectors learned only from the network topology structure are not desirable vectors. For example, in the social network, if two users share some common tags or topics, they are likely to be similar but topologically far apart. Thus, topology-based network representation learning methods cannot effectively capture their similarity. In such a case, other types of heterogeneous information should be incorporated to learn node representation vectors of better quality. Therefore, the researchers propose some representation learning methods that utilize both the network topology and heterogeneous information to learn node representation vectors, such as CANE [9], CNRL [10], and PPNE [11]. Nevertheless, most existing network representation learning methods are designed for traditional networks with pairwise relationships, wherein each edge only links one pair of nodes. However, the relationships among the data objects in the real world are much morecomplex and often not necessarily pairwise. For example, it forms a high-order relation <[PERSON], movie, war> that [PERSON] watches a war movie. The network that captures the high-order relationship is often referred to as the hypernetwork. In view of the above facts, the researchers extend the spectral clustering technique [12] to hypergraphs [13] to propose a series of methods [14; 15; 16]. However, these methods mainly aim at homogeneous hypernetworks, which construct the hyperedges through potential similarities such as common tags. As for the heterogeneous hypernetwork, tensor decomposition [17; 18] can be directly applied to learn node representation vectors, but the time complexity of tensor decomposition is often too high to effectively scale to large-scale hypernetworks. HGNN [19] is a hypergraph neural network model for data representation learning. However, the datasets to evaluate this model is not real hypernetwork datasets, but traditional network datasets. HPHG [20] proposes a deep model named as hyper-gram to learn low-dimensional representation vectors, but the hyperedge is not sufficiently considered in this model so that the hypernetwork topology structure cannot be well preserved. DHNE [21] provides a solution for modeling hyperedges directly without hyperedge decomposition. However, due to the neural network structure used in this method, this method is limited to heterogeneous hyperedges of fixed type and fixed size, and the relationship between multiple types of objects of unfixed size cannot be considered. In view of the above facts, this paper proposes a universal hypernetwork representation learning framework, which can effectively encode both the hypernetwork topology structure and hyperedge information (which is handled by solving the following challenge). It is not easy how to combine the hypernetwork topology structure and the hyperedges well into a unified representation learning process under a universal framework.