# X-GOAL: Multiplex Heterogeneous Graph Prototypical Contrastive Learning

arXiv: https://arxiv.org/abs/2109.03560 · HTML: https://mlsanity.com/paper/2109.03560/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 77 references that are in the map.
- First posted on arXiv 8 Sep 2021.

## Builds on (most cited first, 30 of 43)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [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)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Structural Deep Clustering Network](https://mlsanity.com/paper/2002.01633/) (2020)
- [Self-supervised Heterogeneous Graph Neural Network with Co-contrastive Learning](https://mlsanity.com/paper/2105.09111/) (2021)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)

## Built on by (most cited first, 19 of 19)

- [HiGPT: Heterogeneous Graph Language Model](https://mlsanity.com/paper/2402.16024/) (2024)
- [Heterogeneous Contrastive Learning for Foundation Models and Beyond](https://mlsanity.com/paper/2404.00225/) (2024)
- [COIN: Co-Cluster Infomax for Bipartite Graphs](https://mlsanity.com/paper/2206.00006/) (2022)
- [PyG-SSL: A Graph Self-Supervised Learning Toolkit](https://mlsanity.com/paper/2412.21151/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [Learning Individual Treatment Effects under Heterogeneous Interference in Networks](https://mlsanity.com/paper/2210.14080/) (2022)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Cluster Aware Graph Anomaly Detection](https://mlsanity.com/paper/2409.09770/) (2024)
- [Fairness-aware Multi-view Clustering](https://mlsanity.com/paper/2302.05788/) (2023)
- [ARIEL: Adversarial Graph Contrastive Learning](https://mlsanity.com/paper/2208.06956/) (2022)
- [GC-Flow: A Graph-Based Flow Network for Effective Clustering](https://mlsanity.com/paper/2305.17284/) (2023)
- [Unsupervised Multiplex Graph Learning with Complementary and Consistent Information](https://mlsanity.com/paper/2308.01606/) (2023)
- [Automated Contrastive Learning Strategy Search for Time Series](https://mlsanity.com/paper/2403.12641/) (2024)
- [A Geometric Perspective for High-Dimensional Multiplex Graphs](https://mlsanity.com/paper/2501.17374/) (2025)
- [Gaussian Graph with Prototypical Contrastive Learning in E-Commerce Bundle Recommendation](https://mlsanity.com/paper/2307.13468/) (2023)
- [Generating QM1B with PySCFIPU](https://mlsanity.com/paper/2311.01135/) (2023)
- [LAMP: Learnable Meta-Path Guided Adversarial Contrastive Learning for Heterogeneous Graphs](https://mlsanity.com/paper/2409.06323/) (2024)
- [Modeling Heterophily in Multiplex Graphs: An Adaptive Approach for Node Classification](https://mlsanity.com/paper/2605.12699/) (2026)

## Abstract (arXiv)

Graphs are powerful representations for relations among objects, which have attracted plenty of attention. A fundamental challenge for graph learning is how to train an effective Graph Neural Network (GNN) encoder without labels, which are expensive and time consuming to obtain. Contrastive Learning (CL) is one of the most popular paradigms to address this challenge, which trains GNNs by discriminating positive and negative node pairs. Despite the success of recent CL methods, there are still two under-explored problems. First, how to reduce the semantic error introduced by random topology based data augmentations. Traditional CL defines positive and negative node pairs via the node-level topological proximity, which is solely based on the graph topology regardless of the semantic information of node attributes, and thus some semantically similar nodes could be wrongly treated as negative pairs. Second, how to effectively model the multiplexity of the real-world graphs, where nodes are connected by various relations and each relation could form a homogeneous graph layer. To solve these problems, we propose a novel multiplex heterogeneous graph prototypical contrastive leaning (X-GOAL) framework to extract node embeddings. X-GOAL is comprised of two components: the GOAL framework, which learns node embeddings for each homogeneous graph layer, and an alignment regularization, which jointly models different layers by aligning layer-specific node embeddings. Specifically, the GOAL framework captures the node-level information by a succinct graph transformation technique, and captures the cluster-level information by pulling nodes within the same semantic cluster closer in the embedding space. The alignment regularization aligns embeddings across layers at both node and cluster levels. We evaluate X-GOAL on various real-world datasets and downstream tasks to demonstrate its effectiveness.