A Fast Network Embedding Approach with Preserving Hierarchical Proximities

Network embedding projects nodes in a network to a low-dimensional continuous space while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to its significant progress in network learning tasks, such as node classification, link prediction, and visualization. However, many network embedding works focus on the pairwise co-occurrence to depict nodes' proximity and suffer from the expensive computations due to the large volume of networks. In this paper, we take into consideration the multiple step hitting probability to model hierarchical proximities, and propose a fast and scalable spectral network embedding method, NetPHP, which learns different order embeddings and can be trained faster than SGD based methods. To evaluate the performance, we conduct the multi-label classification experiments in different large-scale real networks. The empirical results demonstrate the NetPHP algorithm outperforms other state-of-the-art methods. Besides, we also investigate the effect of different order proximities and non-adjacent node's proximities.