Abstract: Scientists study trajectory data to understand trends in movement patterns, such as human mobility for traffic analysis and urban planning. In this paper, we introduce a novel trajectory clustering technique whose central idea is to use vector fields to induce a notion of similarity between trajectories, letting the vector fields themselves define and represent each cluster. We present an efficient algorithm to find a locally optimal clustering of trajectories into vector fields, and demonstrate how vector-field k-means can find patterns missed by previous methods. We present experimental evidence of its effectiveness and efficiency using several datasets, including historical hurricane data, GPS tracks of people and vehicles, and anonymous cellular radio handoffs from a large service provider.