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Within the context of Graph Signal Processing (GSP), Graph Learning (GL) isconcerned with the inference of the graph's underlying structure from nodalobservations. However, real-world data often contains diverse information,necessitating the simultaneous clustering and learning of multiple graphs. Inpractical applications, valuable node-specific covariates, represented askernels, have been underutilized by existing graph signal clustering methods.In this letter, we propose a new framework, named Kernel-based joint MultipleGL and clustering of graph signals (KMGL), that leverages a multi-convexoptimization approach. This allows us to integrate node-side information,construct low-pass filters, and efficiently solve the optimization problem. Theexperiments demonstrate that KMGL significantly enhances the robustness of GLand clustering, particularly in scenarios with high noise levels and asubstantial number of clusters. These findings underscore the potential of KMGLfor improving the performance of GSP methods in diverse, real-worldapplications.

Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals