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  .
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 .
R
When exploring large time-varying data sets
The availability of devices that track moving objects has led to an explosive growth in trajectory data. When exploring the resulting large trajectory collections
D
for further consideration
R
data elements
spatial positions of the tracked objects
D
in a compact one-dimensional form or
R
. Such 1D representations
; visualizations of such orderings
R
1D representation
ordering
R
1D representations
orderings
R
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
In this paper we introduce a new
R
method is explicitly parametrized
(SPC) method to compute such orderings, which is explicitly parameterized
A
extensive
D
1D
R
our
ours and other
R
our stable algorithms outperform
stable dimensionality reduction outperforms
A
; in particular, our new SPC method does so at a fraction of the computational costs