LAUSR

Multi-order proximity is useful for effective network embedding. In contrast to many previous works that only consider order-level weights, this paper proposes to explore a more expressive node-level weighting mechanism to encode the diverse local structure, with a scalable and theoretically justified sampling strategy for its learning. Specifically, we start with a formal definition of multi-order proximity matrix which leads to our new multi-order objective based on Laplacian Eigenmaps and Skip-Gram. Then we instantiate the node-specific multi-order weights in the objective with the help of neighborhood size estimation, which indicates node-specific multi-order information. For objective learning, it is implicitly fulfilled with our proposed branching tree-like random walk strategy termed by BTWalk, which differs from the dominant chain-like walk in existing sampling techniques. BTWalk is designed by a synergetic combination of BFS (breadth-first search) and DFS (depth-first search), which is modulated according to the weights of the considered proximity orders. We theoretically analyze its cost-efficiency, and further propose the so-called Vec4Cross framework that incorporates joint node embedding and network alignment for two partially overlapped networks based on the seed matchings, whereby BTWalk is also adopted for embedding. Promising experimental results are obtained on real-world datasets across popular tasks.