Efficient and Robust Graph Metric Learning Guided by Model Selection Principles

Graph Metric Learning (GML) is increasingly critical for tasks such as classification, clustering, and anomaly detection on graph-structured data. However, selecting an optimal model that balances accuracy, and computational efficiency remains a core challenge. While existing works have integrated information-theoretic criteria such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with graph neural networks (e.g., Liu et al.), this study advances the state-of-the-art by presenting a unified, model-agnostic framework that systematically combines AIC/BIC with diverse GML techniques. Our proposed approach, Graph Metric Learning with Model Selection (GMLMS), begins by generating a candidate pool comprising traditional metric learning methods (e.g., LMNN, ITML), graph neural networks, and kernel-based models. Each candidate is evaluated based on its AIC and BIC scores to identify the model that best balances fit and complexity. The selected model is then fine-tuned to enhance performance. Experimental evaluation on real-world datasets, including citation networks, social graphs, and protein-protein interaction networks, demonstrates that GML-MS significantly outperforms individual baseline methods. The selected model achieved the highest accuracy (94.2%) with improved precision, recall, and F1-score, while also maintaining the lowest AIC and BIC values. This work provides a robust, scalable, and interpretable solution for graph learning applications, especially where large-scale, complex data necessitates careful model selection for optimal performance.