When exploring large time-varying data sets, visual summaries are a useful tool to identify time intervals of interest for further consideration. A typical approach is to represent the data elements at each time step in a compact one-dimensional form or via a one-dimensional ordering. Such 1D representations 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 1D representation capture the structure of the data at each time step, and stability -- how coherent are the 1D representations over consecutive time steps or temporal ranges? We focus on techniques that create such visual summaries for entities moving in 2D. Previous work has considered only the creation of 1D orderings, using spatial subdivisions and clustering techniques. In contrast, we propose to use actual dimensionality-reduction techniques to compute stable and spatially informative 1D representations. These more general 1D representations provide the user with additional visual cues describing the spatial distribution of the data, and naturally imply also a 1D ordering. To make dimensionality-reduction techniques suitable for visual summaries, we introduce stable variants of Principle Component Analysis, Sammon mapping, and t-SNE. Our Stable Principal Component method is explicitly parametrized for stability, allowing a trade-off between the spatial quality and stability. We conduct computational experiments that quantitatively compare the 1D orderings produced by our 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 our stable algorithms outperform existing methods on stability, without sacrificing spatial quality or efficiency.
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