BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation

Abstract

Dimensionality reduction (DR) is a popular approach to data exploration in which instances in a given dataset are mapped to a lower-dimensional representation or “embedding.” For nonlinear dimensionality reduction (NLDR), the dimensions of the embedding may be difficult to understand. In such cases, it may be useful to learn how the different dimensions relate to a set of external features (i.e., relevant features that were not used for the DR). A variety of methods (e.g., PROFIT and BIR) use external features to explain embeddings generated by NLDR methods with rotation-invariant objective functions, such as multidimensional scaling (MDS). However, these methods are restricted to two-dimensional embeddings. In this paper, we propose BIOT, which makes it possible to explain an MDS embedding with any number of dimensions without requiring visualization.