Within the context of Graph Signal Processing (GSP), Graph Learning (GL) is
concerned with the inference of a graph's topology from nodal observations,
i.e., graph signals. However, data is often in mixed form, relating to
different underlying structures. This heterogeneity necessitates the joint
clustering and learning of multiple graphs. In many real-life applications,
there are available node-side covariates (i.e., kernels) that imperatively
should be incorporated, which has not been addressed by the rare graph signal
clustering approaches. To this end and inspired by the rich K-means framework,
we propose a novel kernel-based algorithm to incorporate this node-side
information as we jointly partition the signals and learn a graph for each
cluster. Numerical experiments demonstrate its effectiveness over the
state-of-the-art.

在图信号处理（GSP）的背景下，图学习（GL）关注的是从节点观测（即图信号）中推断出图的拓扑结构。然而，数据通常是混合形式，涉及不同的底层结构。这种异质性需要对多个图进行联合聚类和学习。在许多现实应用中，节点侧协变量（即核函数）是可用的，并且必须被纳入考虑，而这并没有在现有的图信号聚类方法中得到解决。为此，受到丰富的 K-means 框架的启发，我们提出了一种新颖的基于核函数的算法，用于在同时对信号进行分区和为每个簇学习一个图的过程中将节点侧信息纳入考虑。数值实验证明了它相比于现有技术的有效性。