Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph representations. In this paper we propose a novel TDL-based method for compressing signals over graphs, consisting in two main steps: first, disjoint sets of higher-order structures are inferred based on the original signal --by clustering $N$ datapoints into $K\ll N$ collections; then, a topological-inspired message passing gets a compressed representation of the signal within those multi-element sets. Our results show that our framework improves both standard GNN and feed-forward architectures in compressing temporal link-based signals from two real-word Internet Service Provider Networks' datasets --from $30\%$ up to $90\%$ better reconstruction errors across all evaluation scenarios--, suggesting that it better captures and exploits spatial and temporal correlations over the whole graph-based network structure.

翻译：近期兴起的拓扑深度学习（TDL）方法旨在通过自然处理高阶交互，超越图表示所定义的成对关系和局部邻域，从而扩展当前的图神经网络（GNN）。本文提出一种基于TDL的图信号压缩新方法，包含两个主要步骤：首先，根据原始信号推断出不相交的高阶结构集合——通过将N个数据点聚类为K<<N个分组；随后，基于拓扑启发的消息传递机制在这些多元素集合内获取信号的压缩表示。实验结果表明，该方法在压缩两个真实互联网服务提供商网络数据集的时序链路信号时，优于标准GNN和前馈架构——在所有评估场景中重建误差降低30%至90%——这表明它能更有效地捕获和利用基于图的全网络结构中的时空关联性。