从平滑信号中学习克罗内克结构图，建模复杂依赖关系。
Learning Kronecker-Structured Graphs from Smooth Signals
- 通过交替优化分解因子图，解决克罗内克图学习的非凸难题。
- 在合成与真实数据上优于现有方法，尤其在复杂依赖场景下表现更优。
- 适合处理多维异构数据中的耦合关系建模，如社交网络或生物网络。
图学习（或网络推断）是图信号处理（GSP）中的核心问题。GSP将傅里叶变换推广至非欧几里得域，而当这些域未知时，图学习至关重要。随着多维度数据日益普遍，产品图因其能自然分解多维依赖关系而受到关注。然而，现有可学习的产品图类型仍难以刻画多样化的依赖结构。本文研究从平滑信号中学习克罗内克结构产品图的问题。相较于常见的笛卡尔积，克罗内克积以更复杂、不可分离的方式建模依赖，但对图学习提出更高约束。针对此非凸问题，我们提出一种交替优化方案，分别更新每个因子图，并提供渐近收敛性理论保证。算法还被扩展用于学习强积结构的因子图。在合成与真实图数据上的实验表明，该方法有效且显著优于现有方法。
原文摘要 · Abstract (English)
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 unknown. 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 and provide theoretical guarantees for its asymptotic convergence. The proposed algorithm is also modified to learn factor graphs of the strong product. We conduct experiments on synthetic and real-world graphs and demonstrate our approach's efficacy and superior performance compared to existing methods.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。