论文标题
来自层间耦合的多属性图形信号的产品图形学习
Product Graph Learning from Multi-attribute Graph Signals with Inter-layer Coupling
论文作者
论文摘要
本文考虑从多属性图形信号学习产品图。我们的工作是由多层网络的广泛存在的动机，这些网络在图层内和跨图层中具有相互作用。专注于具有均匀层的产品图设置，我们提出了双变量多项式图滤波器模型。然后，我们考虑通过适应现有光谱方法的拓扑推理问题。我们为所需的光谱估计步骤提出了两种解决方案：通过将多属性数据展开到矩阵中的简化解决方案，以及通过最近的Kronecker产品分解（NKD）的精确解决方案。有趣的是，我们表明，强层间耦合可以降低展开解决方案的性能，而NKD解决方案对层间耦合效应具有鲁棒性。数值实验显示了我们方法的功效。
This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph setting with homogeneous layers, we propose a bivariate polynomial graph filter model. We then consider the topology inference problems thru adapting existing spectral methods. We propose two solutions for the required spectral estimation step: a simplified solution via unfolding the multi-attribute data into matrices, and an exact solution via nearest Kronecker product decomposition (NKD). Interestingly, we show that strong inter-layer coupling can degrade the performance of the unfolding solution while the NKD solution is robust to inter-layer coupling effects. Numerical experiments show efficacy of our methods.
