  Due to the massively increasing amount of available geospatial data and the
need to present it in an understandable way, clustering this data is more
important than ever. As clusters might contain a large number of objects,
having a representative for each cluster significantly facilitates
understanding a clustering. Clustering methods relying on such representatives
are called center-based. In this work we consider the problem of center-based
clustering of trajectories.
  In this setting, the representative of a cluster is again a trajectory. To
obtain a compact representation of the clusters and to avoid overfitting, we
restrict the complexity of the representative trajectories by a parameter l.
This restriction, however, makes discrete distance measures like dynamic time
warping (DTW) less suited.
  There is recent work on center-based clustering of trajectories with a
continuous distance measure, namely, the Fr\'echet distance. While the
Fr\'echet distance allows for restriction of the center complexity, it can also
be sensitive to outliers, whereas averaging-type distance measures, like DTW,
are less so. To obtain a trajectory clustering algorithm that allows
restricting center complexity and is more robust to outliers, we propose the
usage of a continuous version of DTW as distance measure, which we call
continuous dynamic time warping (CDTW). Our contribution is twofold:
  1. To combat the lack of practical algorithms for CDTW, we develop an
approximation algorithm that computes it.
  2. We develop the first clustering algorithm under this distance measure and
show a practical way to compute a center from a set of trajectories and
subsequently iteratively improve it.
  To obtain insights into the results of clustering under CDTW on practical
data, we conduct extensive experiments.
