# Graph Representation Learning Beyond Node and Homophily

arXiv: https://arxiv.org/abs/2203.01564 · HTML: https://mlsanity.com/paper/2203.01564/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Adversarially Regularized Graph Autoencoder for Graph Embedding](https://mlsanity.com/paper/1802.04407/) (2018)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Is a Single Embedding Enough? Learning Node Representations that Capture Multiple Social Contexts](https://mlsanity.com/paper/1905.02138/) (2019)

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

- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Multi-View Graph Representation Learning Beyond Homophily](https://mlsanity.com/paper/2304.07509/) (2023)

## Abstract (arXiv)

Unsupervised graph representation learning aims to distill various graph information into a downstream task-agnostic dense vector embedding. However, existing graph representation learning approaches are designed mainly under the node homophily assumption: connected nodes tend to have similar labels and optimize performance on node-centric downstream tasks. Their design is apparently against the task-agnostic principle and generally suffers poor performance in tasks, e.g., edge classification, that demands feature signals beyond the node-view and homophily assumption. To condense different feature signals into the embeddings, this paper proposes PairE, a novel unsupervised graph embedding method using two paired nodes as the basic unit of embedding to retain the high-frequency signals between nodes to support node-related and edge-related tasks. Accordingly, a multi-self-supervised autoencoder is designed to fulfill two pretext tasks: one retains the high-frequency signal better, and another enhances the representation of commonality. Our extensive experiments on a diversity of benchmark datasets clearly show that PairE outperforms the unsupervised state-of-the-art baselines, with up to 101.1% relative improvement on the edge classification tasks that rely on both the high and low-frequency signals in the pair and up to 82.5% relative performance gain on the node classification tasks.