Reconstructing High-Dimensional Datasets From Their Bivariate Projections
This addresses a data reconstruction challenge for researchers and practitioners in data visualization and analysis, but it is incremental as it builds on existing projection techniques.
The paper tackles the problem of reconstructing high-dimensional datasets from their bivariate projections, introducing graph-based methods like clique-finding to generate possible rows, and shows high success in recreating significant portions of datasets for random and real-world cases, with failure factors including lower dimension, higher n, and lower interval.
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.