This paper presents a new approach for assembling graph neural networks based
on framelet transforms. The latter provides a multi-scale representation for
graph-structured data. We decompose an input graph into low-pass and high-pass
frequencies coefficients for network training, which then defines a
framelet-based graph convolution. The framelet decomposition naturally induces
a graph pooling strategy by aggregating the graph feature into low-pass and
high-pass spectra, which considers both the feature values and geometry of the
graph data and conserves the total information. The graph neural networks with
the proposed framelet convolution and pooling achieve state-of-the-art
performance in many node and graph prediction tasks. Moreover, we propose
shrinkage as a new activation for the framelet convolution, which thresholds
high-frequency information at different scales. Compared to ReLU, shrinkage
activation improves model performance on denoising and signal compression:
noises in both node and structure can be significantly reduced by accurately
cutting off the high-pass coefficients from framelet decomposition, and the
signal can be compressed to less than half its original size with
well-preserved prediction performance.

本文提出了一种基于框架变换的组装图神经网络的新方法，该方法将输入图分解成低通和高通频率系数用于网络训练，定义了一种基于框架的图卷积。使用此方法，图神经网络在节点和图预测任务中取得了最先进的性能，并且我们提出使用收缩作为框架卷积的新激活函数，与 ReLU 相比，收缩激活函数能够在降噪和信号压缩方面显著提高模型的性能。