# GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding

arXiv: https://arxiv.org/abs/1910.02370 · HTML: https://mlsanity.com/paper/1910.02370/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

## Built on by (most cited first, 30 of 58)

- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [New Benchmarks for Learning on Non-Homophilous Graphs](https://mlsanity.com/paper/2104.01404/) (2021)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Local Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2109.03856/) (2021)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Contrastive Laplacian Eigenmaps](https://mlsanity.com/paper/2201.05493/) (2022)
- [Equivariant Graph Hierarchy-Based Neural Networks](https://mlsanity.com/paper/2202.10643/) (2022)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Network Representation Learning: From Preprocessing, Feature Extraction to Node Embedding](https://mlsanity.com/paper/2110.07582/) (2021)
- [A Survey on Graph Neural Network Acceleration: Algorithms, Systems, and Customized Hardware](https://mlsanity.com/paper/2306.14052/) (2023)
- [Hierarchical Transformer for Scalable Graph Learning](https://mlsanity.com/paper/2305.02866/) (2023)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Influence-Based Mini-Batching for Graph Neural Networks](https://mlsanity.com/paper/2212.09083/) (2022)
- [GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networks](https://mlsanity.com/paper/2201.12741/) (2022)
- [Hierarchical graph neural nets can capture long-range interactions](https://mlsanity.com/paper/2107.07432/) (2021)
- [Graph Coarsening via Convolution Matching for Scalable Graph Neural Network Training](https://mlsanity.com/paper/2312.15520/) (2023)
- [A Topology-aware Graph Coarsening Framework for Continual Graph Learning](https://mlsanity.com/paper/2401.03077/) (2024)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Diversified Multiscale Graph Learning with Graph Self-Correction](https://mlsanity.com/paper/2103.09754/) (2021)
- [Query Driven-Graph Neural Networks for Community Search: From Non-Attributed, Attributed, to Interactive Attributed](https://mlsanity.com/paper/2104.03583/) (2021)
- [Large-Scale Network Embedding in Apache Spark](https://mlsanity.com/paper/2106.10620/) (2021)
- [MultiBiSage: A Web-Scale Recommendation System Using Multiple Bipartite Graphs at Pinterest](https://mlsanity.com/paper/2205.10666/) (2022)
- [HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering](https://mlsanity.com/paper/2210.14813/) (2022)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [Learning Based Proximity Matrix Factorization for Node Embedding](https://mlsanity.com/paper/2106.05476/) (2021)

## Abstract (arXiv)

Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data. However, existing graph embedding models either fail to incorporate node attribute information during training or suffer from node attribute noise, which compromises the accuracy. Moreover, very few of them scale to large graphs due to their high computational complexity and memory usage. In this paper we propose GraphZoom, a multi-level framework for improving both accuracy and scalability of unsupervised graph embedding algorithms. GraphZoom first performs graph fusion to generate a new graph that effectively encodes the topology of the original graph and the node attribute information. This fused graph is then repeatedly coarsened into much smaller graphs by merging nodes with high spectral similarities. GraphZoom allows any existing embedding methods to be applied to the coarsened graph, before it progressively refine the embeddings obtained at the coarsest level to increasingly finer graphs. We have evaluated our approach on a number of popular graph datasets for both transductive and inductive tasks. Our experiments show that GraphZoom can substantially increase the classification accuracy and significantly accelerate the entire graph embedding process by up to 40.8x, when compared to the state-of-the-art unsupervised embedding methods.