Graph-CBMKL: A Clustering-Based Multiple Kernel Learning Framework for Graph Neural Networks

Graph neural networks (GNNs) have recently emerged as a dominant paradigm for representation learning on graphstructured data. However, most existing GNNs rely on a single predefined similarity metric or adjacency assumption, which restricts their ability to model heterogeneous relations and leads to suboptimal generalization under sparse or noisy graph conditions. Multiple kernel learning (MKL), on the other hand, provides a principled mechanism for fusing complementary similarity measures but has rarely been integrated with deep graph architectures in a theoretically grounded manner. To bridge this gap, we propose Graph-CBMKL, a novel Clustering-Based Multiple Kernel Learning framework that unifies kernel fusion and graph representation learning within an end-to-end differentiable GNN. Specifically, the model employs a convex combination of diverse base kernels to adaptively weight node-wise similarities, while a clustering-guided regularizer encourages compact and semantically consistent embedding spaces. The alternating optimization scheme jointly updates kernel weights and GNN parameters, with provable convergence and bounded computational complexity through low-rank approximations. This design transforms kernel weight learning into a convex subproblem embedded within a non-convex deep model, achieving a unique balance between interpretability and expressiveness. Comprehensive experiments on three benchmark citation networks (Cora, Citeseer, and PubMed) verify the superiority of Graph-CBMKL. The model consistently outperforms both classical GNNs (e.g., GCN, GAT) and recent MKL-based graph frameworks in terms of accuracy, macro-F1, and stability. Notably, GraphCBMKL shows substantial advantages in low-sample and sparse-topology regimes, demonstrating strong robustness to noise and improved clustering quality of latent embeddings. The results collectively confirm that incorporating multikernel fusion with structural clustering offers a new and effective perspective for advancing graph neural network research, providing a scalable and theoretically sound foundation for heterogeneous graph representation learning.