  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.
