  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.
