# Topological Graph Signal Compression

arXiv: https://arxiv.org/abs/2308.11068 · HTML: https://mlsanity.com/paper/2308.11068/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 21 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Signal-to-Noise Ratio: A Robust Distance Metric for Deep Metric Learning](https://mlsanity.com/paper/1904.02616/) (2019)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [Understanding Mobile Traffic Patterns of Large Scale Cellular Towers in Urban Environment](https://mlsanity.com/paper/1510.04026/) (2015)
- [Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes](https://mlsanity.com/paper/2210.14758/) (2022)
- [Characterizing the Latent Space of Molecular Deep Generative Models with Persistent Homology Metrics](https://mlsanity.com/paper/2010.08548/) (2020)
- [Leveraging Spatial and Temporal Correlations for Network Traffic Compression](https://mlsanity.com/paper/2301.08962/) (2023)

## Abstract (arXiv)

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 Kll 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.