Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals
This work addresses the need for more robust graph learning and clustering in real-world applications with diverse data, though it appears incremental by building on existing methods.
The paper tackled the problem of simultaneously learning multiple graphs and clustering graph signals in Graph Signal Processing by integrating node-specific covariates via kernels, resulting in enhanced robustness, especially under high noise and many clusters.
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.