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.

我们提出了一种新的方法来估计图的拓扑，并识别三节点的相互作用，通过结构化的图 Volterra 核来学习二阶简单复形 (SCs)，通过使用群规范和掩膜矩阵求解图和 SC 推理的数学公式，实验结果表明我们的方法在合成和真实数据上具有优越性能。