# Learning Structural Node Embeddings Via Diffusion Wavelets

arXiv: https://arxiv.org/abs/1710.10321 · HTML: https://mlsanity.com/paper/1710.10321/

## Key facts

- Cited by 97 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 27 Oct 2017.

## Built on by (most cited first, 30 of 97)

- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Twitch Gamers: a Dataset for Evaluating Proximity Preserving and Structural Role-based Node Embeddings](https://mlsanity.com/paper/2101.03091/) (2021)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [Network Representation Learning: From Preprocessing, Feature Extraction to Node Embedding](https://mlsanity.com/paper/2110.07582/) (2021)
- [Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs](https://mlsanity.com/paper/2103.14187/) (2021)
- [Source Free Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2112.00955/) (2021)
- [Generalizable Cross-Graph Embedding for GNN-based Congestion Prediction](https://mlsanity.com/paper/2111.05941/) (2021)
- [When to Pre-Train Graph Neural Networks? From Data Generation Perspective!](https://mlsanity.com/paper/2303.16458/) (2023)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Graph Structural Attack by Perturbing Spectral Distance](https://mlsanity.com/paper/2111.00684/) (2021)
- [Graph Reinforcement Learning for Combinatorial Optimization: A Survey and Unifying Perspective](https://mlsanity.com/paper/2404.06492/) (2024)
- [A Broader Picture of Random-walk Based Graph Embedding](https://mlsanity.com/paper/2110.12344/) (2021)
- [A survey and taxonomy of loss functions in machine learning](https://mlsanity.com/paper/2301.05579/) (2023)
- [Better with Less: A Data-Active Perspective on Pre-Training Graph Neural Networks](https://mlsanity.com/paper/2311.01038/) (2023)
- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [Graph Embedding via Diffusion-Wavelets-Based Node Feature Distribution Characterization](https://mlsanity.com/paper/2109.07016/) (2021)
- [Node Proximity Is All You Need: Unified Structural and Positional Node and Graph Embedding](https://mlsanity.com/paper/2102.13582/) (2021)
- [Spectral Augmentations for Graph Contrastive Learning](https://mlsanity.com/paper/2302.02909/) (2023)
- [The Autodidactic Universe](https://mlsanity.com/paper/2104.03902/) (2021)
- [Calibrating and Improving Graph Contrastive Learning](https://mlsanity.com/paper/2101.11525/) (2021)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [Geometric Multimodal Deep Learning with Multi-Scaled Graph Wavelet Convolutional Network](https://mlsanity.com/paper/2111.13361/) (2021)
- [Trace Encoding in Process Mining: a survey and benchmarking](https://mlsanity.com/paper/2301.02167/) (2023)
- [Few-Shot Causal Representation Learning for Out-of-Distribution Generalization on Heterogeneous Graphs](https://mlsanity.com/paper/2401.03597/) (2024)
- [Learning Based Proximity Matrix Factorization for Node Embedding](https://mlsanity.com/paper/2106.05476/) (2021)

## Abstract (arXiv)

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%.