Unsupervised Multiple Kernel Learning for Graphs via Ordinality Preservation

Learning effective graph similarities is crucial for tasks like clustering, yet selecting the optimal kernel to evaluate such similarities in unsupervised settings remains a major challenge. Despite the development of various graph kernels, determining the most appropriate one for a specific task is particularly difficult in the absence of labeled data. Existing methods often struggle to handle the complex structure of graph data and rely on heuristic approaches that fail to adequately capture the global relationships between graphs. To overcome these limitations, we propose Unsupervised Multiple Kernel Learning for Graphs (UMKL-G 1 ), a model that combines multiple graph kernels without requiring labels or predefined local neighbors. Our approach preserves the topology of the data by maintaining ordinal relationships among graphs through a probability simplex, allowing for a unified and adaptive kernel learning process. We provide theoretical guarantees on the stability, robustness, and generalization of our method. Empirical results demonstrate that UMKL-G outperforms individual kernels and other state-of-theart methods, offering a robust solution for unsupervised graph analysis.