Before revision:  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.
After revision:  In this paper we introduce a new Stable Principal Component method is explicitly parametrized for stability, allowing a trade-off between the spatial quality and stability.