# HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning

arXiv: https://arxiv.org/abs/2405.14742 · HTML: https://mlsanity.com/paper/2405.14742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [When Does Self-Supervision Help Graph Convolutional Networks?](https://mlsanity.com/paper/2006.09136/) (2020)
- [InfoGCL: Information-Aware Graph Contrastive Learning](https://mlsanity.com/paper/2110.15438/) (2021)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [Rethinking pooling in graph neural networks](https://mlsanity.com/paper/2010.11418/) (2020)
- [Evaluating Graph Neural Networks for Link Prediction: Current Pitfalls and New Benchmarking](https://mlsanity.com/paper/2306.10453/) (2023)
- [Generative and Contrastive Self-Supervised Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2108.09896/) (2021)
- [On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks](https://mlsanity.com/paper/2212.02374/) (2022)
- [Hard Sample Aware Network for Contrastive Deep Graph Clustering](https://mlsanity.com/paper/2212.08665/) (2022)
- [Learning Hierarchical Protein Representations via Complete 3D Graph Networks](https://mlsanity.com/paper/2207.12600/) (2022)
- [Heterogeneous Graph Masked Autoencoders](https://mlsanity.com/paper/2208.09957/) (2022)
- [Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering](https://mlsanity.com/paper/2305.02931/) (2023)
- [Self-supervised Training of Graph Convolutional Networks](https://mlsanity.com/paper/2006.02380/) (2020)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [Graph Convolutional Neural Networks based on Quantum Vertex Saliency](https://mlsanity.com/paper/1809.01090/) (2018)
- [Image Classification using Graph Neural Network and Multiscale Wavelet Superpixels](https://mlsanity.com/paper/2201.12633/) (2022)

## Abstract (arXiv)

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.