Learning Structural Node Embeddings Via Diffusion Wavelets
This addresses the challenge of automatically capturing structural roles in networks for machine learning tasks, offering a scalable solution with significant performance gains, though it is incremental as it builds on diffusion-based methods.
The paper tackles the problem of learning structural node embeddings in graphs to identify similar roles across different network parts, developing GraphWave, an unsupervised method using heat wavelet diffusion patterns that scales linearly with edges and outperforms existing baselines by up to 137% in experiments.
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 be used for a variety of machine learning tasks. However, learning structural representations of nodes is a challenging problem, and it has typically involved manually specifying and tailoring topological features for each node. In this paper, we develop GraphWave, a method that represents each node's network neighborhood via a low-dimensional embedding by leveraging heat wavelet diffusion patterns. Instead of training on hand-selected features, GraphWave learns these embeddings in an unsupervised way. We mathematically prove that nodes with similar network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network, and our method scales linearly with the number of edges. Experiments in a variety of different settings demonstrate GraphWave's real-world potential for capturing structural roles in networks, and our approach outperforms existing state-of-the-art baselines in every experiment, by as much as 137%.