1 code implementation • 25 Nov 2021 • Florian Frantzen, Jean-Baptiste Seby, Michael T. Schaub
Here we consider trajectories as edge-flow vectors defined on a simplicial complex, a higher-order generalization of graphs, and use the Hodge 1-Laplacian of the simplicial complex to derive embeddings of these edge-flows.
no code implementations • 14 Jun 2021 • Michael T. Schaub, Jean-Baptiste Seby, Florian Frantzen, T. Mitchell Roddenberry, Yu Zhu, Santiago Segarra
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i. e., the higher-order or multi-way relations connecting the constituent entities.
no code implementations • 14 Jan 2021 • Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby, T. Mitchell Roddenberry, Santiago Segarra
In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing.