Auto-GG: Autonomous Grouping of Data with Non-Convex Geometries via Planar Graphs

Cluster analysis is a fundamental task in unsupervised learning and essential for identifying intrinsic structures in datasets. However, traditional approaches face significant limitations, such as the need for prior definition of the number of clusters and difficulty in handling non-convex geometries. This paper proposes Auto-GG, an autonomous clustering algorithm based on Gabriel Graphs. The methodology uses the graph as a topological skeleton and applies the elbow method to the edge weight distribution to automatically determine the optimal cut threshold. Experiments conducted with synthetic datasets of complex shapes demonstrate that Auto-GG outperforms K-Means in external validation metrics, such as ARI and NMI. The study concludes that the integration of computational geometry allows for the disclosure of the data's natural structure without dependency on subjective hyperparameters.