Topological Graph Signal Compression
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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≪ 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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