Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can also be used to inform machine learning on graphs. However, learning structural representations of nodes is a challenging unsupervised-learning task, which typically involves manually specifying and tailoring topological features for each node. Here we develop GraphWave, a method that represents each node's local network neighborhood via a low-dimensional embedding by leveraging spectral graph wavelet diffusion patterns. We prove that nodes with similar local network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network. Our method scales linearly with the number of edges and does not require any hand-tailoring of topological features. We evaluate performance on both synthetic and real-world datasets, obtaining improvements of up to 71% over state-of-the-art baselines.

本文介绍了GraphWave方法，通过利用热波中的扩散模式，表示每个节点的网络邻域，并以无监督的方式学习这些嵌入。本文证明，具有类似网络邻域的节点将具有类似的GraphWave嵌入，即使这些节点可能位于网络的非常不同的部分，该方法在捕捉网络中的结构角色方面有着很高的潜力，并且在实验中表现出优秀的性能，超过了现有的所有基线方法，最高达到137%。

通过扩散小波学习结构节点嵌入