Topological Graph Signal Compression

• URL: http://arxiv.org/abs/2308.11068v2
• Date: Tue, 5 Dec 2023 13:42:53 GMT
• Title: Topological Graph Signal Compression
• Authors: Guillermo Bern\'ardez, Lev Telyatnikov, Eduard Alarc\'on, Albert Cabellos-Aparicio, Pere Barlet-Ros, Pietro Li\`o
• Abstract summary: We propose a novel TDL-based method for compressing signals over graphs. Our results show that our framework improves both standard GNN and feed-forward architectures.
• Score: 7.836468889756101
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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