Stable Trajectory Clustering: An Efficient Split and Merge Algorithm

Clustering algorithms fundamentally group data points by characteristics to identify patterns. Over the past two decades, researchers have extended these methods to analyze trajectories of humans, animals, and vehicles, studying their behavior and movement across applications. \noindent This paper presents whole-trajectory clustering and sub-trajectory clustering algorithms based on DBSCAN line segment clustering, which encompasses two key events: split and merge of line segments. The events are utilized to capture object movement history based on the average Euclidean distance between line segments. In this framework, whole-trajectory clustering considers entire entities' trajectories, whereas sub-trajectory clustering employs a sliding window model to identify local similarity patterns. Many existing trajectory clustering algorithms respond to temporary anomalies in data by splitting trajectories, which often obscures otherwise consistent clustering patterns and leads to less reliable insights. To address this, we introduce the stable trajectory clustering algorithm, which leverages the mean absolute deviation concept to demonstrate that selective omission of transient deviations not only preserves the integrity of clusters but also improves their stability and interpretability. We evaluate all proposed algorithms on real trajectory datasets to illustrate their effectiveness and sensitivity to parameter variations.