Abstract
<title>Abstract</title> <p>Clustering complex data remains challenging in the presence of nonconvex structures, varying densities, and noise.In this paper, We propose a Front Propagation–Based Clustering (FP) framework that formulates cluster formation as a competitive propagation process over a neighborhood graph, governed by density-modulated speeds and arrival-time dynamics. The framework unifies two complementary algorithms: Adaptive Front Propagation Clustering (AFP), which propagates labels using locally adaptive speeds derived from neighborhood density, and Arrival-Time Front Propagation Clustering (ATFP), which assigns points based on exact shortest-path arrival times, yielding deterministic and geometrically consistent partitions. Unlike classical density-based clustering, cluster membership is determined by propagation dynamics rather than by thresholding density estimates. By modeling clusters as regions reached by competing propagation fronts, FP naturally handles arbitrary cluster shapes and noise without global optimization or sensitive thresholds. Extensive experiments on synthetic and real-world benchmark datasets demonstrate that the proposed methods consistently achieve high accuracy and robustness, outperforming or matching state-of-the-art clustering algorithms such as DBSCAN, k-means, and HDBSCAN. These results establish front propagation as an effective and interpretable paradigm for graph-based clustering.</p>