# Embedding Graphs on Grassmann Manifold

arXiv: https://arxiv.org/abs/2205.15068 · HTML: https://mlsanity.com/paper/2205.15068/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 69 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Bilinear CNNs for Fine-grained Visual Recognition](https://mlsanity.com/paper/1504.07889/) (2015)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)

## Built on by (most cited first, 2 of 2)

- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [Matrix Manifold Neural Networks++](https://mlsanity.com/paper/2405.19206/) (2024)

## Abstract (arXiv)

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's similarity relationship in the embedded space needs specific tools and a similarity metric. This paper develops a new graph representation learning scheme, namely EGG, which embeds approximated second-order graph characteristics into a Grassmann manifold. The proposed strategy leverages graph convolutions to learn hidden representations of the corresponding subspace of the graph, which is then mapped to a Grassmann point of a low dimensional manifold through truncated singular value decomposition (SVD). The established graph embedding approximates denoised correlationship of node attributes, as implemented in the form of a symmetric matrix space for Euclidean calculation. The effectiveness of EGG is demonstrated using both clustering and classification tasks at the node level and graph level. It outperforms baseline models on various benchmarks.