Using Fourier analysis, we explore the robustness and vulnerability of graph convolutional neural networks (GCNs) for skeleton-based action recognition. We adopt a joint Fourier transform (JFT), a combination of the graph Fourier transform (GFT) and the discrete Fourier transform (DFT), to examine the robustness of adversarially-trained GCNs against adversarial attacks and common corruptions. Experimental results with the NTU RGB+D dataset reveal that adversarial training does not introduce a robustness trade-off between adversarial attacks and low-frequency perturbations, which typically occurs during image classification based on convolutional neural networks. This finding indicates that adversarial training is a practical approach to enhancing robustness against adversarial attacks and common corruptions in skeleton-based action recognition. Furthermore, we find that the Fourier approach cannot explain vulnerability against skeletal part occlusion corruption, which highlights its limitations. These findings extend our understanding of the robustness of GCNs, potentially guiding the development of more robust learning methods for skeleton-based action recognition.

翻译：利用傅里叶分析，我们探讨了基于骨架的动作识别中图卷积神经网络（GCNs）的鲁棒性与脆弱性。我们采用联合傅里叶变换（JFT），即图傅里叶变换（GFT）与离散傅里叶变换（DFT）的结合，研究经对抗训练后的GCNs在面对对抗攻击与常见干扰时的鲁棒性。基于NTU RGB+D数据集的实验结果表明，对抗训练并未引发对抗攻击与低频扰动之间的鲁棒性权衡——这种权衡在基于卷积神经网络的图像分类中通常存在。这一发现表明，在基于骨架的动作识别中，对抗训练是一种增强对对抗攻击与常见干扰鲁棒性的实用方法。此外，我们发现傅里叶方法无法解释针对骨架局部部分遮挡干扰的脆弱性，这凸显了其局限性。这些发现拓展了我们对GCNs鲁棒性的理解，可能为开发更鲁棒的基于骨架的动作识别方法提供指导。