Non-maximum suppression (NMS) is a key post-processing step in many computer vision applications. In the context of object detection, it is used to transform a smooth response map that triggers many imprecise object window hypotheses in, ideally, a single bounding-box for each detected object. The most common approach for NMS for object detection is a greedy, locally optimal strategy with several hand-designed components (e.g., thresholds). Such a strategy inherently suffers from several shortcomings, such as the inability to detect nearby objects. In this paper, we try to alleviate these problems and explore a novel formulation of NMS as a well-defined clustering problem. Our method builds on the recent Affinity Propagation Clustering algorithm, which passes messages between data points to identify cluster exemplars. Contrary to the greedy approach, our method is solved globally and its parameters can be automatically learned from training data. In experiments, we show in two contexts - object class and generic object detection - that it provides a promising solution to the shortcomings of the greedy NMS.