Topological Graph Signal Compression

TL;DR

This paper introduces a topological deep learning method for graph signal compression that leverages higher-order structures to significantly improve reconstruction accuracy over traditional GNNs.

Contribution

It proposes a novel TDL-based approach that infers higher-order structures and uses topological message passing for efficient signal compression on graphs.

Findings

Achieves 30% to 90% better reconstruction errors than standard GNNs.

Effectively captures spatial and temporal correlations in network data.

Improves compression of link-based signals in real-world ISP datasets.

Abstract

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.