Topology, Signal processing and Applications
- Michael Schaub
Abstract
We present topology aware signal processing tools [1] for the representation of simplicial complexes and cell complexes and signals defined on these. Specifically we discuss how harmonic flow embeddings that exploit topology offer a unified, interpretable framework for dynamic and static (edge-flow) data on complexes, and can be used for sparse representation tasks [2], outlier detection [3] and classification of trajectories [4,5].
References
[1] Schaub, M.T.; Zhu, Y.; Seby, J.-B.; Roddenberry, T.M. & Segarra, S. (2021), "Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond", Signal Processing., January, 2021. Vol. 187, pp. 108149.
[2] Hoppe, J. & Schaub, M.T. (2024), "Representing Edge Flows on Graphs via Sparse Cell Complexes", In Proceedings of the Second Learning on Graphs Conference., June, 2024. Vol. 231, pp. 1:1-1:22. PMLR.
[3] Frantzen, F. & Schaub, M.T. (2025), "HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection", In Proceedings of the 31st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2025)., August, 2025.
[4] Frantzen, F.; Seby, J.-B. & Schaub, M.T. (2021), "Outlier Detection for Trajectories via Flow-embeddings", In 2021 55th Asilomar Conference on Signals, Systems, and Computers., October, 2021. , pp. 1568-1572.
[5] Grande, V.P.; Hoppe, J.; Frantzen, F. & Schaub, M.T. (2024), "Topological Trajectory Classification and Landmark Inference on Simplicial Complexes", In 58th Annual Asilomar Conference on Signals, Systems, and Computers., October, 2024. , pp. 44-48.
