Simplicial Complex Learning from Edge Flows via Sparse Clique Sampling

We focus on learning simplicial complexes, which are higher-order generalizations of graphs, from edge flow data. We propose a probabilistic model for edge flow signals that captures the influence of node and triangle signals on the edge- based signals along with the structure of the underlying simplicial complex. We formulate simplicial complex learning as a sparse clique sampling problem. We then learn the filled triangles, latent node, and triangle signals using a maximum a posteriori estimation procedure. We validate our model through experiments on synthetic and real-world transportation datasets, demonstrating its effectiveness in identifying the higher-order structure and capturing the relationship between edge flows and signals over nodes and triangles.