  The availability of devices that track moving objects has led to an explosive
growth in trajectory data. When exploring the resulting large trajectory
collections, visual summaries are a useful tool to identify time intervals of
interest. A typical approach is to represent the spatial positions of the
tracked objects at each time step via a one-dimensional ordering;
visualizations of such orderings can then be placed in temporal order along a
time line. There are two main criteria to assess the quality of the resulting
visual summary: spatial quality -- how well does the ordering capture the
structure of the data at each time step, and stability -- how coherent are the
orderings over consecutive time steps or temporal ranges? In this paper we
introduce a new Stable Principal Component (SPC) method to compute such
orderings, which is explicitly parameterized for stability, allowing a
trade-off between the spatial quality and stability. We conduct extensive
computational experiments that quantitatively compare the orderings produced by
ours and other stable dimensionality-reduction methods to various
state-of-the-art approaches using a set of well-established quality metrics
that capture spatial quality and stability. We conclude that stable
dimensionality reduction outperforms existing methods on stability, without
sacrificing spatial quality or efficiency; in particular, our new SPC method
does so at a fraction of the computational costs.
