Purpose

UMAP is a ubiquitous tool for low-dimensional visualization of high-dimensional datasets. UMAP learns a low-dimensional mapping from the nearest-neighbor graph structure of a dataset, often producing visually distinct clusters of data that align with known labels (e.g., cell types in a gene expression dataset). While the learned relationship between the input features and the embedding positions can be useful, the nonlinear UMAP embedding function also makes it difficult to directly interpret the mapping in terms of the input features.

Here, we show how to enable interpretation of the nonlinear mapping through a modification of the parametric UMAP approach, which learns the embedding with a deep network that is locally linear (but still globally nonlinear) with respect to the input features. This allows for the computation of a set of exact feature contributions as linear weights that determine the embedding of each data point. By computing the exact feature contribution for each point in a dataset, we directly quantify which features are most responsible for forming each cluster in the embedding space. We explore the feature contributions for a gene expression dataset from this “glass-box” augmentation of UMAP and compare them with features found by differential expression.