SOM-GAT: Topological graph clustering via Self-Organizing Maps and Graph Attention Networks

Self-Organizing Maps (SOM) preserve topological structure through competitive learning but lack adaptive relational reasoning, while Graph Attention Networks (GAT) excel at learning feature-dependent neighborhoods yet remain sensitive to noisy graph inputs. This paper bridges these complementary strengths through SOM-GAT, a hybrid architecture that unifies topology-preserving compression with attention-driven representation learning for unsupervised clustering. The model first projects high-dimensional data onto a fixed SOM grid, generating prototypes enriched with local density and variance statistics. A sparse graph constructed from the lattice topology enables subsequent GAT layers to refine these prototypes through learnable attention weights. We theoretically prove that GAT attention can approximate the continuous positive neighborhood kernel, including the fixed SOM function, to arbitrary precision, while learning strictly more expressive data-adaptive relationships. Clustering is performed via a self-training objective on the refined embeddings. A detailed hyperparameter sensitivity analysis is performed to assess the impact of the SOM grid size, GAT learning rate, and hidden dimension on the effectiveness of the clustering algorithm and the stability of the model. Empirical evaluation across nine benchmark datasets spanning images, sensor records, text, and citation networks demonstrates that SOM-GAT achieves state-of-the-art accuracy on six datasets while maintaining competitive structural metrics. The framework exhibits 76.7% increased inter-prototype similarity with positive information gain ( + 0 . 6828 bits), converges faster than baseline GAT with smoother optimization trajectories, and retains 94.9% of clustering performance under 20% label noise. Statistical significance tests confirm substantial accuracy improvements over traditional spectral approaches and several deep graph clustering methods, while delivering structural performance comparable to leading autoencoder-based techniques. By eliminating reliance on reconstruction objectives and preserving a stable topological layout throughout training, SOM-GAT establishes a principled approach to interpretable, noise-robust graph clustering.