Dual-structure community preserving network embedding.

Network embedding, an effective method for learning low-dimensional representations of nodes, plays a crucial role in various network learning scenarios. However, existing network embedding learning methods fail to learn node embeddings from the perspective of the implicit network, leading to embeddings that only incorporate neighborhood details from neighboring nodes across various levels. In this paper, we propose a network embedding model based on the non-negative matrix factorization (NMF) framework, called Dual-structure Community Preserving Network Embedding (DCPNE), where the dual-structure means that it not only considers the explicit structure of the network, but also constructs the implicit structure of the network. The main benefit is that DCPNE empowers the embedding of nodes to comprehend the dual structure of the network and broadens the embedding information of a node from its neighborhood to its community. Furthermore, we develop an updating rule for optimizing DCPNE, and analyze the time complexity of our model. The results of the experiment on eight real network datasets show that the proposed model performs better than the mainstream algorithms.