Clustering of Gaussian Random Vector Fields in Multiple Trajectory Modelling

This paper concerns the estimation of multiple dynamical models from a set of observed trajectories. It proposes vector valued gaussian random fields, representing dynamical models and their vector fields, combined with a modified k-means clustering algorithm to assign observed trajectories to models. The assignment is done according to a likelihood function obtained from applying the random field associated to a cluster, to the data. The algorithm is shown to have several advantages when compared with others: 1) it does not depend on a grid, region of interest, grid resolution or interpolation method; 2) the estimated vector fields has an associated uncertainty which is given by the algorithm and taken into account. The paper presents results obtained on synthetic trajectories that illustrate the performance of the proposed algorithm.