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This paper presents an approach to the problem of automatically classifying events detected by video surveillance systems; specifically, of detecting unusual or suspicious movements. Approaches to this problem typically involve building complex 3D-models in real-world co-ordinates to provide trajectory information for the classifier. In this paper, we show that analysis of trajectories may be carried out in a model-free fashion, using self-organizing feature map neural networks to learn the characteristics of normal trajectories, and to detect novel ones. Trajectories are represented in 2D image co-ordinates. First and second order motion information is also generated, with moving-average smoothing. This allows novelty detection to be applied on a point-by-point basis in real time, and permits both instantaneous motion and whole trajectory motion to be subjected to novelty detection.