Rotation invariant GPS trajectory mining

Mining of GPS trajectories of moving vehicles and devices can provide valuable insights into urban systems, planning and operational applications. Understanding object motion often requires that the spatial-temporal matching of trajectories be invariant to shifting, scaling and rotation. To this end, Procrustes analysis enables to transform one data set of a trajectory to represent another set of data as closely as possible. We propose a novel shift-scale-rotation invariant Procrustes distance metric based on the Kabsch algorithm, which calculates the optimal rotation matrix by minimizing the root-mean squared deviation between two paired sets of points of trajectories or trajectory segments. We present two novel runtime efficient algorithms which are based on our proposed distance metric: 1) the sliding-shifting-scaling-Kabsch-rotation (S3KR) algorithm for detecting recurring short query patterns in longer motion trajectories and 2) a novel time series subsequence clustering algorithm to group GPS trajectory data and to discover prototypical patterns. We demonstrate the potential of our proposed sliding Procrustes analysis algorithms by applying it on real-world GPS trajectories collected in urban and rural areas from different transport modes, as well as on nautical GPS trajectories. We also demonstrate that our methods outperform the state of the art in accuracy and runtime on synthetic and real world data.