Gauging-$\delta$δ: A Non-Parametric Hierarchical Clustering Algorithm

The development of a nonparametric and versatile clustering algorithm has been a longstanding challenge in unsupervised learning due to the exploratory nature of the clustering problem. This study presents a novel algorithm, named Gauging-$\delta$, which can handle diverse cluster shapes and operate in a nonparametric manner. The algorithm employs a hierarchical merging process that starts from individual data points until no further clusters can be merged. The central component of Gauging-$\delta$ is the adaptive mergeability function, which progressively determines if two clusters are mergeable considering the perceptual statistics of the clusters and their environment. Empirical evaluations on 105 synthetic datasets demonstrate the superiority of the proposed algorithm, particularly in accurately handling well-separated clusters. Experiments on real-world datasets highlight the impact of selecting appropriate data features and distance metrics on clustering results.