# Mix Dimension in Poincar'e Geometry for 3D Skeleton-based Action Recognition

arXiv: https://arxiv.org/abs/2007.15678 · HTML: https://mlsanity.com/paper/2007.15678/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 14 of 14)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Skeleton-Contrastive 3D Action Representation Learning](https://mlsanity.com/paper/2108.03656/) (2021)
- [Learning Skeletal Graph Neural Networks for Hard 3D Pose Estimation](https://mlsanity.com/paper/2108.07181/) (2021)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Skeleton-based Action Recognition via Adaptive Cross-Form Learning](https://mlsanity.com/paper/2206.15085/) (2022)
- [Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Space](https://mlsanity.com/paper/2305.18797/) (2023)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [Bipartite Graph Reasoning GANs for Person Pose and Facial Image Synthesis](https://mlsanity.com/paper/2211.06719/) (2022)
- [Autoencoding Hyperbolic Representation for Adversarial Generation](https://mlsanity.com/paper/2201.12825/) (2022)
- [Hyperbolic Geometry in Computer Vision: A Survey](https://mlsanity.com/paper/2304.10764/) (2023)
- [EHGCN: Hierarchical Euclidean-Hyperbolic Fusion via Motion-Aware GCN for Hybrid Event Stream Perception](https://mlsanity.com/paper/2504.16616/) (2025)
- [Multi-Order Hyperbolic Graph Convolution and Aggregated Attention for Social Event Detection](https://mlsanity.com/paper/2502.00351/) (2025)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have already demonstrated their powerful ability to model the irregular data, e.g., skeletal data in human action recognition, providing an exciting new way to fuse rich structural information for nodes residing in different parts of a graph. In human action recognition, current works introduce a dynamic graph generation mechanism to better capture the underlying semantic skeleton connections and thus improves the performance. In this paper, we provide an orthogonal way to explore the underlying connections. Instead of introducing an expensive dynamic graph generation paradigm, we build a more efficient GCN on a Riemann manifold, which we think is a more suitable space to model the graph data, to make the extracted representations fit the embedding matrix. Specifically, we present a novel spatial-temporal GCN (ST-GCN) architecture which is defined via the Poincar'e geometry such that it is able to better model the latent anatomy of the structure data. To further explore the optimal projection dimension in the Riemann space, we mix different dimensions on the manifold and provide an efficient way to explore the dimension for each ST-GCN layer. With the final resulted architecture, we evaluate our method on two current largest scale 3D datasets, i.e., NTU RGB+D and NTU RGB+D 120. The comparison results show that the model could achieve a superior performance under any given evaluation metrics with only 40% model size when compared with the previous best GCN method, which proves the effectiveness of our model.