Reconstructing High-Dimensional Datasets From Their Bivariate
  Projections
Eli Dugan Klaus Mueller
This paper deals with developing techniques for the reconstruction of
high-dimensional datasets given each bivariate projection, as would be found in
a matrix scatterplot. A graph-based solution is introduced, involving
clique-finding, providing a set of possible rows that might make up the
original dataset. Complications are discussed, including cases where phantom
cliques are found, as well as cases where an exact solution is impossible.
Additional methods are shown, with some dealing with fully deducing rows and
others dealing with having to creatively produce methods that find some
possibilities to be more likely than others. Results show that these methods
are highly successful in recreating a significant portion of the original
dataset in many cases - for randomly generated and real-world datasets - with
the factors leading to a greater rate of failure being lower dimension, higher
n, and lower interval.