Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models that extract features from graph data, and are amenable to generalization and stability analyses. The price paid by GSTs is exponential complexity in space and time that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the exponential complexity associated with GSTs. Stability of the novel pGSTs is also established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, it is shown that graph data in different domains call for different network architectures, and that the pruning algorithm may be employed to guide the design choices for contemporary GCNs.

中文翻译：

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通过剪枝实现高效稳定的图散射变换


图卷积网络（GCN）在各种图学习任务中具有良好的性能记录，但它们的分析仍处于起步阶段。图散射变换 (GST) 提供免训练的深度 GCN 模型，可以从图数据中提取特征，并且适合泛化和稳定性分析。 GST 付出的代价是空间和时间的指数复杂性，随着层数的增加而增加。当需要深层架构时，这会阻碍 GST 的部署。目前的工作通过引入一种有效的所谓修剪 (p)GST 方法来解决 GST 的复杂性限制。由此产生的修剪算法以图谱启发的标准为指导，并动态保留信息丰富的散射特征，同时绕过与 GST 相关的指数复杂性。当输入图数据或网络结构受到扰动时，新型 pGST 的稳定性也得以建立。此外，还通过分析和实验研究了 pGST 对随机和局部信号扰动的敏感性。数值测试表明，pGST 的性能与基线 GST 相当，并且节省了相当多的计算量。此外，pGST 在图形和 3D 点云分类任务中实现了与最先进的 GCN 相当的性能。通过分析 pGST 剪枝模式，发现不同领域的图数据需要不同的网络架构，并且剪枝算法可以用来指导当代 GCN 的设计选择。