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Found 8 papers, 4 papers with code
Topological Trajectory Classification and Landmark Inference on Simplicial Complexes
Specifically, given a set of labelled trajectories, which we interpret as edge-flows on the underlying simplicial complex, we search for 2-simplices whose deletion results in an optimal separation of the trajectory labels according to the corresponding spectral embedding of the trajectories into the harmonic space.
Learning From Simplicial Data Based on Random Walks and 1D Convolutions
Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hypergraphs and simplicial complexes.
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes.
Signal Processing on Product Spaces
We establish a framework for signal processing on product spaces of simplicial and cellular complexes.
Outlier Detection for Trajectories via Flow-embeddings
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.
Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes
We first show that the Hodge Laplacian can be used in lieu of the graph Laplacian to construct a family of wavelets for higher-order signals on simplicial complexes.
Signal processing on simplicial complexes
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.
The Effects of Randomness on the Stability of Node Embeddings
We systematically evaluate the (in-)stability of state-of-the-art node embedding algorithms due to randomness, i. e., the random variation of their outcomes given identical algorithms and graphs.
