基于核的多图联合学习与图信号聚类
Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals
AI总结：
针对现有图信号聚类方法未充分利用节点协变量的问题，提出基于核的多图联合学习与图信号聚类框架KMGL，采用多凸优化整合节点信息，显著提升高噪声、多聚类场景下的鲁棒性。
摘要：
在图信号处理（Graph Signal Processing, GSP）的研究背景下，图学习（Graph Learning, GL）旨在从节点观测值中推断图的底层结构。然而，现实世界的数据往往包含多样化信息，因此需要同时对多个图进行聚类和学习。在实际应用中，以核函数形式表示的、有价值的节点特定协变量，尚未被现有的图信号聚类方法充分利用。在这篇论文中，我们提出了一个名为基于核的多图联合学习与图信号聚类（Kernel-based joint Multiple GL and clustering of graph signals, KMGL）的新框架，该框架采用多凸优化方法。这使得我们能够整合节点侧信息、构建低通滤波器，并高效求解优化问题。实验表明，KMGL显著提升了图学习和聚类的鲁棒性，尤其是在高噪声水平和聚类数量较多的场景下。这些发现凸显了KMGL在各类现实应用中提升图信号处理方法性能的潜力。
英文摘要：
Within the context of Graph Signal Processing (GSP), Graph Learning (GL) is concerned with the inference of the graph's underlying structure from nodal observations. However, real-world data often contains diverse information, necessitating the simultaneous clustering and learning of multiple graphs. In practical applications, valuable node-specific covariates, represented as kernels, have been underutilized by existing graph signal clustering methods. In this letter, we propose a new framework, named Kernel-based joint Multiple GL and clustering of graph signals (KMGL), that leverages a multi-convex optimization approach. This allows us to integrate node-side information, construct low-pass filters, and efficiently solve the optimization problem. The experiments demonstrate that KMGL significantly enhances the robustness of GL and clustering, particularly in scenarios with high noise levels and a substantial number of clusters. These findings underscore the potential of KMGL for improving the performance of GSP methods in diverse, real-world applications.
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