ACTGNN: Assessment of Clustering Tendency with Synthetically-Trained Graph Neural Networks

Determining clustering tendency in datasets is a fundamental but challenging task, especially in noisy or high-dimensional settings where traditional methods, such as the Hopkins Statistic and Visual Assessment of Tendency (VAT), often struggle to produce reliable results. In this paper, we propose ACTGNN, a graph-based framework designed to assess clustering tendency by leveraging graph representations of data. Node features are constructed using Locality-Sensitive Hashing (LSH), which captures local neighborhood information, while edge features incorporate multiple similarity metrics, such as the Radial Basis Function (RBF) kernel, to model pairwise relationships. A Graph Neural Network (GNN) is trained exclusively on synthetic datasets, enabling robust learning of clustering structures under controlled conditions. Extensive experiments demonstrate that ACTGNN significantly outperforms baseline methods on both synthetic and real-world datasets, exhibiting superior performance in detecting faint clustering structures, even in high-dimensional or noisy data. Our results highlight the generalizability and effectiveness of the proposed approach, making it a promising tool for robust clustering tendency assessment.