Multi-order Matched Neighborhood Consistent Graph Alignment in a Union Vector Space

In this paper, we study the unsupervised plain graph alignment problem, which aims to find node correspondences across two graphs without any side information. The majority of previous works addressed UPGA based on structural information, which will inevitably lead to subgraph isomorphism issues. That is, unaligned nodes could take similar local structural information. To mitigate this issue, we present the Multi-order Matched Neighborhood Consistent (MMNC) which tries to match nodes by aligning the learned node embeddings with only a small number of pseudo alignment seeds. In particular, we extend matched neighborhood consistency (MNC) to vector space and further develop embedding-based MNC (EMNC). By minimizing the EMNC-based loss function, we can utilize the limited pseudo alignment seeds to approximate the orthogonal transformation matrix between two groups of node embeddings with high efficiency and accuracy. Through extensive experiments on public benchmarks, we show that the proposed methods achieve a good balance between alignment accuracy and speed over multiple datasets compared with existing methods.