Uncertainty embedding of attribute networks based on multi-view information fusion and multi-order proximity preservation

The attribute network embedding process aims to define the low-dimensional continuous vector representation of nodes by fusing the network structure view and the node attribute view, and to preserve the multi-order proximity information of the network in the embedded latent space. However, attribute network contains multi-view information with nonlinear relationships, uncertainty in node representation caused by complex interactions between nodes, and multi-order proximity information in the network structure and node attributes. The reported research has not comprehensively considered the mentioned problems, resulting in poor embedding effect of attribute network. This paper proposes a framework of a ttribute n etwork u ncertainty e mbedding based on multi-view i nformation f usion and multi-order p roximity p reservation (ANUE-VIFPP). ANUE-VIFPP comprehensively extracts the information of network structure view, attribute view and structure-attribute view, which uses the combination of self-attention mechanism and nonlinear layer to fuse the highly nonlinear coupled multi-view information effectively. The normalization flow (NF) algorithm is introduced into variational auto-encoders (VAE) to establish a flexible distribution for characterizing the uncertainty of node representation. A multi-conditional loss function constraint model is developed to effectively preserve the low and high order proximity information of network structure and node attributes in the embedded hidden space. Finally, experimental results obtained on three commonly used real-world datasets demonstrate that ANUEVIFPP performs well in node classification, link prediction, and network visualization tasks, outperforming some state-of-the-art methods.