Nonparametric Dimensionality Reduction Quality Assessment based on Sortedness of Unrestricted Neighborhood

Abstract

High-dimensional data are known to be challenging to explore visually. Dimensionality Reduction (DR) techniques are good options for making high-dimensional data sets more interpretable and computationally tractable. An inherent question regarding their use is how much relevant information is lost during the layout generation process. In this study, we aim to provide means to quantify the quality of a DR layout according to the intuitive notion of sortedness of the data points. For such, we propose a straightforward measure with Kendall t at its core to provide values in a standard and meaningful interval. We present sortedness and pairwise sortedness as suitable replacements over, respectively, trustworthiness and stress when assessing projection quality. The formulation, its rationale and scope, and experimental results show their strength compared to the state-of-the-art.