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 recovered axes are in direct analogy with positional legends of traditional scatterplots, and show how to solve the computational challenges presented by the generalization to non-linear methods. We show how automatic differentiation makes the calculation of such perturbations efficient and can easily be 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 and hyperparameter choices. Finally, we discuss limitations of our proposal and situations where further research is needed.
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