Round-Trip KNN Clustering: multiscale hierarchical cluster detection on directed nearest-neighbour graphs

Eraldo Pereira Marinho, Caetano Mazzoni Ranieri, Fabricio Aparecido Breve

We introduce Round-Trip KNN Clustering (RTKNNC), a graph-based method for finding cluster structure at several neighbourhood scales without requiring the number of clusters in advance. Unlike approaches that first make a $k$-nearest-neighbour (KNN) graph undirected, RTKNNC keeps both directions of the neighbour relation: which points a given point selects and which points select it. Incoming selections are treated as weighted votes that help decide which local connections remain visible during a recursive forward-and-reverse traversal. Repeating the procedure for increasing $K$ reveals how groups persist or merge as the neighbourhood scale grows; for the reference inverse-square model before structural refinement, clusters can merge but do not split. Because graph connectivity can occasionally join distinct groups through a sparse bridge or a small region of overlap, we add an optional label-free refinement. It first tests whether an already formed component is better described by two or three Gaussian subpopulations, and accepts a subdivision only when the proposed groups are large enough and consistent with the visible KNN graph. Across eight synthetic datasets and…