Topological Graph Signal Compression
This work addresses signal compression in graph-based networks, offering a novel approach that could enhance efficiency in domains like Internet Service Provider Networks, though it appears incremental by building on existing TDL methods.
The paper tackles the problem of compressing signals over graphs by proposing a Topological Deep Learning method that clusters data into higher-order structures and uses topological message passing. The results show improvements of 30% to 90% in reconstruction errors compared to standard methods on real-world network datasets.
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.