Self-organizing trajectories

Abstract Trajectories and parameterized curves are data types of growing importance. Many measures for such data have been proposed in order to provide analogues to the mean and variance of vectors. We identify a counterintuitive oscillating behaviour of dynamic time warp-based averages on certain data sets. We present an algorithm that combines ideas from from both self-organizing maps and dynamic time warping that avoids these oscillations and hence promises more representative curve averages. These improvements also allow for accurate estimation of the piece-wise variance for a set of general N-dimensional trajectories. The run-time performance is demonstrated on movement data from rowing, where we are able to provide performance feedback in real-time to users in a simulator.