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Trajectory data are usually recorded as a sequence of sampled data points. For most trajectory data collected from human carried GPS devices (eg, Geolife dataset [32]), the data are collected in a constant sampling rate. Since people travel using di erent transportation modes, the variance of velocities is large, which causes the trajectories to be very sparse in some parts but highly dense in some others. is phenomenon seriously challenges the existing trajectory distance measurements in the following two aspects. First, for sparse parts of the trajectory, although several trajectory distance measures have been developed, it is extremely challenging for the existing trajectory measures to work well when the data points are sparse (eg, GPS data collected on highway) due to the absence of matched points pairs among the trajectories. Second, for highly dense parts in the trajectory, the distance measurement is not scalable to large dataset even using the simplest Euclidean distance measure.

In order to address the above challenges concurrently, we propose a Step-Invariant Trajectory (SIT) representation with linear time translation from raw data to uniformly distributed trajectory points by dynamically changing the sampling rates. Based on SIT representation, we propose two e ective and scalable distance measures which are BMED and PBMED for SIT. We evaluate the e ectiveness and e ciency of our representation along with its distance measures by performing multiple trajectory classication and clustering experiments. ese results show that our distance measures on SITs is much more robust than other distance measures and representations on …