  Comparison is a core task in visual analysis. Although there are numerous
guidelines to help users design effective visualizations to aid known
comparison tasks, there are few techniques available when users want to make ad
hoc comparisons between marks, trends, or charts during data exploration and
visual analysis. For instance, to compare voting count maps from different
years, two stock trends in a line chart, or a scatterplot of country GDPs with
a textual summary of the average GDP. Ideally, users can directly select the
comparison targets and compare them, however what elements of a visualization
should be candidate targets, which combinations of targets are safe to compare,
and what comparison operations make sense? This paper proposes a conceptual
model that lets users compose combinations of values, marks, legend elements,
and charts using a set of composition operators that summarize, compute
differences, merge, and model their operands. We further define a View
Composition Algebra (VCA) that is compatible with datacube-based
visualizations, derive an interaction design based on this algebra that
supports ad hoc visual comparisons, and illustrate its utility through several
use cases.
