  The emerging domain of data-enabled science necessitates development of
algorithms and tools for knowledge discovery. Human interaction with data
through well-constructed graphical representation can take special advantage of
our visual ability to identify patterns. We develop a data visualization
framework, called BiFold, for exploratory analysis of bipartite datasets that
describe binary relationships between groups of objects. Typical data examples
would include voting records, organizational memberships, and pairwise
associations, or other binary datasets. BiFold provides a low dimensional
embedding of data that represents similarity by visual nearness, analogous to
Multidimensional Scaling (MDS). The unique and new feature of BiFold is its
ability to simultaneously capture both within-group and between-group
relationships among objects, enhancing knowledge discovery. We benchmark BiFold
using the {\it Southern Women Dataset}, where social groups are now visually
evident. We construct BiFold plots for two US voting datasets: For the
presidential election outcomes since 1976, BiFold illustrates the evolving
geopolitical structures that underlie these election results. For Senate
congressional voting, BiFold identifies a partisan coordinate, separating
senators into two parties while simultaneously visualizing a
bipartisan-coalition coordinate which captures the ultimate fate of the bills
(pass/fail). Finally, we consider a global cuisine dataset of the association
between recipes and food ingredients. BiFold allows us to visually compare and
contrast cuisines while also allowing identification of signature ingredients
of individual cuisines.
