An efficient complex network embedding model for hierarchical networks

Several models have been proposed for hierarchical network embedding, however, it is difficult to optimize them. In order to improve the accuracy and efficiency of hierarchical network embedding, we propose Hierarchical Complex Network Embedding (HCNE), which embeds hierarchical networks in complex space. The motivation that we utiliz the Euler formula of complex numbers for hierarchical network embedding is this can make the gradient descent algorithm easily work for complex vectors since vectors are non-Euclidean. To preserve the structure of the hierarchical networks well, we consider parent constraint and brother constraint for hierarchical network (tree) when modeling. Furthermore, we derive an accurate upper bound for the relative radius of complex embedding, which makes HCNE scalable into large hierarchical networks. We conducted a series of experiments on 4 hierarchy datasets, and the superiority of the proposed HCNE model is proved on the tasks of network reconstruction, node classification and network visualization. E.g., HCNE outperforms the suboptimal baseline by 5.1% in terms of MAP on Georgetown dataset for the tasks of network reconstruction and by 9.9% in terms of MP on Wordnet dataset for the tasks of node classification.