  Non-linear dimensionality reduction (NDR) methods such as LLE and t-SNE are
popular with visualization researchers and experienced data analysts, but
present serious problems of interpretation. In this paper, we present
DimReader, a technique that recovers readable axes from such techniques.
DimReader is based on analyzing infinitesimal perturbations of the dataset with
respect to variables of interest. The perturbations define exactly how we want
to change each point in the original dataset and we measure the effect that
these changes have on the projection. The recovered axes are in direct analogy
with the axis lines (grid lines) of traditional scatterplots. We also present
methods for discovering perturbations on the input data that change the
projection the most. The calculation of the perturbations is efficient and
easily integrated into programs written in modern programming languages. We
present results of DimReader on a variety of NDR methods and datasets both
synthetic and real-life, and show how it can be used to compare different NDR
methods. Finally, we discuss limitations of our proposal and situations where
further research is needed.
