A subspace constraint based approach for fast hierarchical graph embedding

Hierarchy network, as a type of complex graphs, is widely used in many application scenarios such as social network analysis in web, human resource analysis in e-government, and product recommendation in e-commerce. Hierarchy preserving network embedding is a representation learning method that project nodes into feature space by preserving the hierarchy property of networks. Recently, researches on network embedding are devoted to mining hierarchical structures and profit a lot form it. Among these works, SpaceNE stands out of preserving hierarchy with the help of subspace constraint on the hierarchical subspace system. However, like all other existing works, SpaceNE is based on transductive learning method and is hard to generalize to new nodes. Besides, they have high time complexity and hard to be scalable to large-scale networks. This paper proposes an inductive method, FastHGE to learn node representation more efficiently and generalize to new nodes more easily. As SpaceNE, a hierarchy network is embedded into a hierarchical subspace tree. For upper communities, we exploit transductive learning by preserving inner-subspace proximity of subspace from the same ancestor. For extending to new nodes, we adopt inductive learning to learn representations of leaf nodes. The overall representation of a node is retrieved by concatenating the embedding vectors of all its ancestor communities and the leaf node. By learning the basis vectors of subspace, the computing cost is alleviated from updating many parameters of projection matrices as in SpaceNE. The performance evaluation experiments show that FastHGE outperforms with much fast speed and the same accuracy. For example, in the node classification, FastHGE is nearly 30 times faster than SpaceNE. The source code of FastHGE is available online.