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

Abstract: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 $K=2,\ldots,16$, independent C and Python implementations produced identical partitions in all 120 reference runs. Refinement increased adjusted Rand index from $0.7817$ to $0.9627$ on a variable-density benchmark and from $0.8083$ to $0.9853$ on a sparse-bridge benchmark. Comparisons with seven external clustering methods show competitive performance while preserving a label-free cluster-construction process.

Submitted to Knowledge and Information Systems (KAIS). 32 pages, 6 figures

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2610.06795 [cs.LG]

(or arXiv:2610.06795v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06795 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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