Learning Kronecker-Structured Graphs from Smooth Signals

Changhao Shi, Gal Mishne

Keywords: Graph Topology Inference, Graph Signal Processing, Kronecker Graph Product

Abstract: Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are not known. With the recent prevalence of multi-way data, there has been growing interest in product graphs that naturally factorize dependencies across different ways. However, the types of graph products that can be learned are still limited for modeling diverse dependency structures. In this paper, we study the problem of learning a Kronecker-structured product graph from smooth signals. Unlike the more commonly used Cartesian product, the Kronecker product models dependencies in a more intricate, non-separable way, but posits harder constraints on the graph learning problem. To tackle this non-convex problem, we propose an alternating scheme to optimize each factor graph in turn and provide theoretical guarantees for its asymptotic convergence. We also modify the proposed algorithm to learn graphs of the strong product, a denser graph product that covers the Kronecker product. We conduct experiments on synthetic and real-world graphs and demonstrate our approach's efficacy and superior performance compared to existing methods.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 88