# GraphTER: Unsupervised Learning of Graph Transformation Equivariant Representations via Auto-Encoding Node-wise Transformations

arXiv: https://arxiv.org/abs/1911.08142 · HTML: https://mlsanity.com/paper/1911.08142/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 22 of 22)

- [Self-Supervised Representation Learning: Introduction, Advances and Challenges](https://mlsanity.com/paper/2110.09327/) (2021)
- [Unsupervised Point Cloud Representation Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2202.13589/) (2022)
- [Self-Contrastive Learning with Hard Negative Sampling for Self-supervised Point Cloud Learning](https://mlsanity.com/paper/2107.01886/) (2021)
- [Parameter-Efficient Fine-Tuning in Spectral Domain for Point Cloud Learning](https://mlsanity.com/paper/2410.08114/) (2024)
- [Imperceptible Transfer Attack and Defense on 3D Point Cloud Classification](https://mlsanity.com/paper/2111.10990/) (2021)
- [Isometric 3D Adversarial Examples in the Physical World](https://mlsanity.com/paper/2210.15291/) (2022)
- [Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks](https://mlsanity.com/paper/2202.07261/) (2022)
- [Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing](https://mlsanity.com/paper/2207.13326/) (2022)
- [CP-Net: Contour-Perturbed Reconstruction Network for Self-Supervised Point Cloud Learning](https://mlsanity.com/paper/2201.08215/) (2022)
- [Hierarchical View Predictor: Unsupervised 3D Global Feature Learning through Hierarchical Prediction among Unordered Views](https://mlsanity.com/paper/2108.03743/) (2021)
- [Data Augmentation-free Unsupervised Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2210.02798/) (2022)
- [DHGCN: Dynamic Hop Graph Convolution Network for Self-Supervised Point Cloud Learning](https://mlsanity.com/paper/2401.02610/) (2024)
- [Upsampling Autoencoder for Self-Supervised Point Cloud Learning](https://mlsanity.com/paper/2203.10768/) (2022)
- [Primitive3D: 3D Object Dataset Synthesis from Randomly Assembled Primitives](https://mlsanity.com/paper/2205.12627/) (2022)
- [Self-Supervised Multi-View Learning via Auto-Encoding 3D Transformations](https://mlsanity.com/paper/2103.00787/) (2021)
- [Self-Supervised Graph Representation Learning via Topology Transformations](https://mlsanity.com/paper/2105.11689/) (2021)
- [Self-Supervised Feature Learning from Partial Point Clouds via Pose Disentanglement](https://mlsanity.com/paper/2201.03018/) (2022)
- [Equivariant Deep Dynamical Model for Motion Prediction](https://mlsanity.com/paper/2111.01892/) (2021)
- [PointJEM: Self-supervised Point Cloud Understanding for Reducing Feature Redundancy via Joint Entropy Maximization](https://mlsanity.com/paper/2312.03339/) (2023)
- [Learning Latent Part-Whole Hierarchies for Point Clouds](https://mlsanity.com/paper/2211.07082/) (2022)
- [Hard-Label Black-Box Attacks on 3D Point Clouds](https://mlsanity.com/paper/2412.00404/) (2024)
- [Rethinking Gradient-based Adversarial Attacks on Point Cloud Classification](https://mlsanity.com/paper/2505.21854/) (2025)

## Abstract (arXiv)

Recent advances in Graph Convolutional Neural Networks (GCNNs) have shown their efficiency for non-Euclidean data on graphs, which often require a large amount of labeled data with high cost. It it thus critical to learn graph feature representations in an unsupervised manner in practice. To this end, we propose a novel unsupervised learning of Graph Transformation Equivariant Representations (GraphTER), aiming to capture intrinsic patterns of graph structure under both global and local transformations. Specifically, we allow to sample different groups of nodes from a graph and then transform them node-wise isotropically or anisotropically. Then, we self-train a representation encoder to capture the graph structures by reconstructing these node-wise transformations from the feature representations of the original and transformed graphs. In experiments, we apply the learned GraphTER to graphs of 3D point cloud data, and results on point cloud segmentation/classification show that GraphTER significantly outperforms state-of-the-art unsupervised approaches and pushes greatly closer towards the upper bound set by the fully supervised counterparts. The code is available at: https://github.com/gyshgx868/graph-ter.