A mode-based clustering algorithm without mode seeking

Mode-based clustering approaches such as mean-shift and its variants are extremely successful. They are also computationally expensive due to their iterative hill-climbing strategy when determining cluster labels for samples. We identify the fact that mode-based cluster boundaries exhibit themselves as minor surfaces of the data distribution. Based on this observation, we develop a mode-based clustering methodology that does not involve iterative hill climbing for each sample. The method, instead, is based on searching for the presence of a minor surface on a path that connects pairs of samples. The pairwise data connections, when evaluated efficiently, may lead to a simple graph connectivity matrix based on which clusters can be identified using connected components. This search efficiency is achieved by an agglomerative clustering approach in the particular proposition presented in this paper. Illustrative experiments are carried out on synthetic datasets using Gaussian mixture models and kernel density estimates.