Learning graphs and simplicial complexes from data
Andrei Buciulea Elvin Isufi Geert Leus Antonio G. Marques
Graphs are widely used to represent complex information and signal domains
with irregular support. Typically, the underlying graph topology is unknown and
must be estimated from the available data. Common approaches assume pairwise
node interactions and infer the graph topology based on this premise. In
contrast, our novel method not only unveils the graph topology but also
identifies three-node interactions, referred to in the literature as
second-order simplicial complexes (SCs). We model signals using a graph
autoregressive Volterra framework, enhancing it with structured graph Volterra
kernels to learn SCs. We propose a mathematical formulation for graph and SC
inference, solving it through convex optimization involving group norms and
mask matrices. Experimental results on synthetic and real-world data showcase a
superior performance for our approach compared to existing methods.