# Joint Embedding of Graphs

arXiv: https://arxiv.org/abs/1703.03862 · HTML: https://mlsanity.com/paper/1703.03862/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2017.

## Built on by (most cited first, 12 of 12)

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- [Clustered Graph Matching for Label Recovery and Graph Classification](https://mlsanity.com/paper/2205.03486/) (2022)
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- [Learning Joint and Individual Structure in Network Data with Covariates](https://mlsanity.com/paper/2406.08776/) (2024)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming](https://mlsanity.com/paper/2101.02180/) (2021)
- [Community Detection in Weighted Multilayer Networks with Ambient Noise](https://mlsanity.com/paper/2103.00486/) (2021)
- [Graph-Convolutional Autoencoder Ensembles for the Humanities, Illustrated with a Study of the American Slave Trade](https://mlsanity.com/paper/2401.00824/) (2024)
- [Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings](https://mlsanity.com/paper/2409.17544/) (2024)
- [Tensor State Space-based Dynamic Multilayer Network Modeling](https://mlsanity.com/paper/2506.02413/) (2025)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Matching and mixing: Matchability of graphs under Markovian error](https://mlsanity.com/paper/2601.20020/) (2026)

## Abstract (arXiv)

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.