Topological Graph Signal Compression

Guillermo Bernardez, Lev Telyatnikov, Eduard Alarcon, Albert Cabellos-Aparicio, Pere Barlet-Ros, Pietro Lio

Keywords: Topological Deep Learning, Graph Neural Networks, Compression

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 signals from two real-world 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.

Submission Type: Extended abstract (max 4 main pages).

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Submission Number: 17