# Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognition

arXiv: https://arxiv.org/abs/2104.05482 · HTML: https://mlsanity.com/paper/2104.05482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 61 of its 148 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1611.08050/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Convolutional Two-Stream Network Fusion for Video Action Recognition](https://mlsanity.com/paper/1604.06573/) (2016)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotations](https://mlsanity.com/paper/1704.02463/) (2017)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Spatio-Temporal LSTM with Trust Gates for 3D Human Action Recognition](https://mlsanity.com/paper/1607.07043/) (2016)
- [An End-to-End Spatio-Temporal Attention Model for Human Action Recognition from Skeleton Data](https://mlsanity.com/paper/1611.06067/) (2016)
- [A New Representation of Skeleton Sequences for 3D Action Recognition](https://mlsanity.com/paper/1703.03492/) (2017)

## Abstract (arXiv)

Spectral graph convolutional networks (GCNs) are particular deep models which aim at extending neural networks to arbitrary irregular domains. The principle of these networks consists in projecting graph signals using the eigen-decomposition of their Laplacians, then achieving filtering in the spectral domain prior to back-project the resulting filtered signals onto the input graph domain. However, the success of these operations is highly dependent on the relevance of the used Laplacians which are mostly handcrafted and this makes GCNs clearly sub-optimal. In this paper, we introduce a novel spectral GCN that learns not only the usual convolutional parameters but also the Laplacian operators. The latter are designed "end-to-end" as a part of a recursive Chebyshev decomposition with the particularity of conveying both the differential and the non-differential properties of the learned representations -- with increasing order and discrimination power -- without overparametrizing the trained GCNs. Extensive experiments, conducted on the challenging task of skeleton-based action recognition, show the generalization ability and the outperformance of our proposed Laplacian design w.r.t. different baselines (built upon handcrafted and other learned Laplacians) as well as the related work.