We address the statistical challenge of classifying subjects as hemiplegic, vestibular or normal based on complex trajectories obtained through two experimental protocols which were designed to evaluate potential deficits in postural control. The classification procedure involves a dimension reduction step where the complex trajectories are summarized by finite-dimensional summary measures based on a stochastic process model for a real-valued trajectory. This allows us to retrieve from the trajectories information relative to their temporal dynamic. A leave-one-out evaluation yields a 79% performance of correct classification for a total of n = 70 subjects, with 22 hemiplegic (31%), 16 vestibular (23%) and 32 normal (46%) subjects.